Pith. sign in

REVIEW 4 major objections 7 minor 133 references

Baryon Construction with $\eta^\prime$ Meson Field

T0 review · 4 major / 7 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read One-flavor baryons are vortices on the η′ domain wall, with spin N_c/2.

desk verdict Review of the one-flavor baryon-on-domain-wall program: honest and internally consistent, but the key Lagrangian is conjectural, so the spin-N_c/2 vortices are an attractive hypothesis, not a derivation. read the letter →

arxiv 2501.18159 v2 pith:ZGZK2OBH submitted 2025-01-30 hep-ph hep-thnucl-th

Fan Lin , Yong-Liang Ma This is my paper · ORCID
classification hep-phhep-thnucl-th
keywords baryonη′mesondomainwallChern-Simons-HiggstheoryvortexquantumHalldropletchiralbagmodellevel-rankduality
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to close a gap in topological baryon physics: for a single quark flavor the usual pion-soliton construction fails because the relevant homotopy group is trivial, so one-flavor baryons need a different home. That home is the η′ domain wall, a two-dimensional surface where the η′ meson field jumps between vacua; the paper argues that the wall's effective theory is a Chern–Simons–Higgs theory whose vortex solutions are baryons. A unit vortex carries baryon number one and spin $N_c/2$, matching large-$N_c$ expectations, and higher-winding vortices give multi-baryon states. The same logic, run through particle–vortex duality, turns quarks into vortices with fractional charge $1/N_c$ and fractional statistics, and it ties the wall picture to the chiral bag model by placing confined monopoles inside the bag and a vector-meson field on its surface. If right, the construction supplies a topological origin for one-flavor baryons that the three-dimensional pion-soliton picture cannot provide.

What carries the argument

The load-bearing object is the η′ domain wall and the conjectured Chern–Simons–Higgs theory on it (Eq. 30). The complex scalar $\phi$ is the bosonized quark field, so $\phi^*\phi$ measures quark density; the emergent U(1) gauge field $a_\mu$ is normalized so that its flux measures baryon number; and the level-$N_c$ Chern–Simons term makes vortex charge and flux quantized. The argument then runs on three topological identities for a winding-$n$ vortex: flux $\Phi=2\pi n$, charge $Q=nN_c$, and spin $s=Q\Phi/4\pi=n^2N_c/2$, with baryon number $B=Q/N_c=n$. Particle–vortex duality applied to this Lagrangian produces the dual matter theory whose vortices carry fractional charge $1/N_c$ and fractional statistics, which is how quarks emerge in the wall picture.

What would settle it

Compute the effective theory induced on an η′ domain wall from a QCD-based framework and check whether it contains a U(1) Chern–Simons term at level $N_c$ coupled to a single complex scalar with the assumed normalization; if it does not, or if the vortex spin is anything other than $n^2N_c/2$, the one-flavor baryon-as-vortex identification is ruled out.

Watch

Extended reading notes

Core claim

The paper's central claim is that a one-flavor baryon is a vortex in an effective (2+1)-dimensional Chern–Simons–Higgs theory living on the η′ domain wall. The conjectured Lagrangian of Eq. (30) combines a complex scalar $\phi$ (the bosonized quark density, with $|\phi|^2$ tracking quark number), a U(1) gauge field $a_\mu$ tied to baryon number, a level-$N_c$ Chern–Simons term, and a Higgs-type potential; the authors show that its vortex solutions with winding number $n$ carry flux $\Phi=2\pi n$, topological charge $Q=nN_c$, and spin $s=Q\Phi/4\pi=n^2N_c/2$. With baryon number $B=Q/N_c=n$, unit-winding vortices are identified with one-flavor (anti)baryons and $|n|\ge2$ with multi-baryon structures. Because the Lagrangian scales as $N_c$ while per-color quark density stays finite, vortex size is $O(N_c^0)$, mass $O(N_c)$, and scattering amplitudes match large-$N_c$ baryon behavior. The paper also argues that particle–vortex duality makes quarks vortices of fractional topological charge $1/N_c$ obeying fractional statistics, and that in the chiral bag picture a surface $U(N_f)_{-N_c}$ Chern–Simons field together with a vector-meson field cancels color and baryon leakage.

Load-bearing premise

The load-bearing premise is that the η′ domain wall is described by the conjectured Chern–Simons–Higgs Lagrangian of Eq. (30), a guess that is not derived from QCD and relies on level-rank duality with scalar matter at an assumed non-trivial infrared fixed point; if that guess fails, the vortex baryons and their $N_c/2$ spin do not follow.

Editorial extensions

If this is right

  • A one-flavor baryon becomes a topological soliton on the η′ domain wall, escaping the trivial $\pi_3(U(1))=0$ that blocks pion-field baryons for $N_f=1$.
  • The unit-winding vortex has baryon number $B=1$ and spin $N_c/2$, so a one-flavor baryon in large-$N_c$ QCD would be a spin-$N_c/2$ object.
  • Higher-winding vortices with $|n|\ge2$ describe multi-baryon states with spin $n^2N_c/2$, analogous to multi-soliton configurations in three dimensions.
  • Particle–vortex duality turns quarks into vortices with fractional topological charge $1/N_c$ and fractional statistics, matching the quarks that leak from chiral bags.
  • The chiral bag model needs a surface $U(N_f)_{-N_c}$ Chern–Simons field plus a vector-meson field to cancel color and baryon leakage and to yield the correct total baryon number.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the conjecture is correct, the construction predicts a spin of $N_c/2$ for a one-flavor baryon; for $N_c=3$ that is spin $3/2$, a number a lattice computation of single-flavor baryons could in principle test.
  • A natural extension is to compare the vortex excitation spectrum with high-spin baryon spectra; the paper's multi-flavor vortices carry high spin, and such a comparison could sharpen where skyrmion and vortex descriptions overlap.
  • The central conjecture could be probed by coupling the domain-wall theory to a baryon-number flux and measuring the induced edge mode; the quantum Hall droplet picture predicts one chiral edge mode carrying unit baryon number, which is a sharper signature than the vortex charge alone.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 7 minor

Summary. The paper reviews and develops the proposal that one-flavor baryons can be constructed as topological objects on the η′ domain wall. After reviewing the Skyrme and chiral bag models for N_f ≥ 2, it presents a conjectured Chern–Simons–Higgs theory on the η′ domain wall (Eq. 30), computes the vortex topological charge, flux, spin, and baryon number (Eqs. 36–39), and argues that a unit vortex has spin N_c/2 and therefore represents a baryon. It then extends the picture to N_f > 1 via a truncated U(2) gauge field ansatz (Section 4.2), and connects the construction to a chiral bag model with confined Z_Nc monopoles and surface vector meson fields (Section 5). The paper closes with a discussion of open problems and the conjectural status of the level-rank duality with scalars.

Significance. If the conjectured effective theory is correct, the paper provides a concrete mechanism for baryons as topological solitons in the one-flavor case, unifying the quantum Hall droplet, vortex, and chiral bag pictures and offering testable large-N_c scaling relations. The paper's strengths include explicit, internally consistent topological computations of charge, flux, and spin (Eqs. 36–38), an honest admission of the conjectural status of the duality (Section 6), and a useful clarification that the surface field A should not be directly identified with vector meson fields (end of Section 5.2). However, the central spin prediction depends on an unverified level assignment in the conjectured Lagrangian, and the N_f=2 extension is based on a restrictive ansatz, so the construction is conditional rather than established.

major comments (4)
  1. [§4.1, Eqs. (30) and (38)] The spin prediction s = n^2 N_c/2 in Eq. (38) depends crucially on the Chern–Simons level in the conjectured Lagrangian (30) being exactly N_c. This level is imported from the level-rank duality (28)–(29); however, the paper does not address possible O(1) corrections to the level from matter loops or parity anomalies in 3d Chern–Simons-matter theories. If the effective level is N_c + δ, the unit vortex spin becomes (N_c + δ)/2, and the literal identification with the one-flavor baryon spin fails. Because the abstract presents the spin N_c/2 as the main result, the authors should either justify the exact level (e.g., through a non-renormalization argument or a specific regularization) or explicitly state this as a caveat.
  2. [§4.2, Eqs. (52)–(53)] The multi-flavor extension sets A1_μ = A2_μ = 0 in Eq. (52) as a 'straightforward resolution', but this is an ad hoc truncation of the u(2) gauge field. The subsequent claims that multi-flavor vortices 'inevitably' carry high spins (Eq. (60)) are derived only within this ansatz. Although the paper later notes that LC captures only a specific type of vortex configuration, the general claim about multi-baryon structures needs to be qualified: other configurations with non-zero off-diagonal gauge fields could lead to different spin–charge relations. Please provide a justification for the truncation or restrict the claim to the ansatz considered.
  3. [§5.1] The confinement mechanism in the chiral bag model is based on the conjecture ('one can further conjecture') that quarks inside the bag are modeled as condensed Z_Nc monopoles. All subsequent surface counterterm constructions and the cancellation of color/baryon number leakage (Eqs. (69)–(85)) rely on this dynamical assumption. Since the paper is a review, this conjecture is acceptable, but the presentation should clearly separate the rigorous 1-form gauge invariance argument (which forces a non-trivial surface theory) from the speculative monopole-condensation picture, so that the reader can distinguish established topology from model-dependent dynamics.
  4. [§4, Eqs. (28)–(30)] The derivation of the effective Lagrangian LA relies on the duality SU(N_c)_{-N_f} + N_f fermions ↔ U(N_f)_{N_c} + N_f scalars, which the authors acknowledge in Section 6 assumes a non-trivial infrared fixed point and does not identify the physical content of the scalars. This assumption is the sole basis for the Chern–Simons–Higgs theory (30) and hence for the vortex-baryon identification. The paper should make this conditionality prominent in the abstract and in the opening of Section 4, rather than only in the conclusions, so that the central claim is clearly presented as a conjecture conditional on the duality.
minor comments (7)
  1. [§2.1, before Eq. (7)] Please define the gamma-matrix convention used for the quark coupling, since the meaning of γ5 in 3+1 dimensions is standard but the sign convention is not specified.
  2. [§4.1, after Eq. (34)] The text says 'the vertex mass, radius' but should read 'the vortex mass, radius'.
  3. [§5.1, after Eq. (67)] 'This simplies' is a typo for 'This implies'.
  4. [§4.2, Eq. (52)] The statement that three of the four gauge fields become massive is not immediately apparent from the displayed mass matrix; please show the diagonalization or clarify.
  5. [§5.2, Eq. (81)] The text says this is 'the same as Equation (44)', but Eq. (44) is the Abelian dual theory; please rephrase to avoid confusion.
  6. [Abstract and Introduction] Both 'meta-stable' and 'metastable' are used; please choose one spelling for consistency.
  7. [§6] The connection to chiral-scale effective theory is mentioned only briefly; if kept, please provide a specific citation where the assumed non-perturbative infrared fixed point is discussed.

Circularity Check

0 steps flagged · score 0.0 of 10

Central vortex-spin result is a conditional topological consequence of an explicitly conjectured Lagrangian, with the N_c level imported from external level-rank duality; no circular reduction found.

full rationale

The paper's key numerical claim, that a unit vortex on the eta-prime domain wall has spin N_c/2 and baryon number one, is not obtained by fitting or by renaming an input. It is a direct consequence of the conjectured Chern-Simons-Higgs Lagrangian in Eq. (30): the U(1) Chern-Simons level N_c gives charge Q = nN_c and flux Phi = 2*pi*n in Eqs. (36)-(37), so the anyon spin s = Q*Phi/(4*pi) = n^2*N_c/2 follows identically, and B = Q/N_c = n uses the standard baryon composition of N_c quarks. The coefficient N_c is not fitted to baryon data; it is imported from the level-rank/bosonization duality (28)-(29), which the paper cites to external work [41,42]. The N_c scaling of vortex mass and radius follows from the power counting chosen in Eqs. (31) and (40) and is presented as consistency evidence, not as an independent derivation of the spin. The paper also explicitly flags the main limitation in Section 6: the scalar field's physical content is unidentified and the duality presumes a non-trivial infrared fixed point. That is an unverified assumption, and a possible level shift would alter the spin prediction, but that is a correctness risk rather than circularity. Self-citations [44,46] summarize the authors' prior proposals, but the present text does not invoke them as an external uniqueness theorem or use them to forbid alternatives; the central derivation is self-contained once Eq. (30) is granted. No step in the claimed derivation chain reduces by definition to its own output, so no significant circularity is present.

Assumptions & free parameters 3 free parameters · 6 assumptions · 4 invented entities

The central vortex-baryon claim rests on a chain of conjectured effective theories: the eta-prime domain-wall Chern-Simons theory, level-rank duality with matter, and the Chern-Simons-Higgs Lagrangian. The N_c scaling of the Lagrangian is chosen by hand in Eqs. (31) and (40), and the monopole and surface vector-meson fields are additional speculative ingredients. No parameter is fitted to experimental data, but the model has several unconstrained scales and no falsifiable prediction that would test the core identification.

free parameters (3)
  • v (vacuum expectation value scale) = unspecified, positive constant
    Introduced in Eq. (31) through V(phi* phi) = N_c sum c_I ((phi* phi / N_c) - v^2)^I. It sets the vortex scale and the per-color quark density. It is not fitted to data and does not affect topological charges.
  • c_I (Higgs potential coefficients) = unspecified, constrained only to give a nonzero VEV
    Coefficients of the potential in Eq. (31). They control local vortex properties such as mass and radius, but not the topological spin or charge, and are chosen by hand.
  • winding numbers n1, n2 (N_f = 2 extension) = integers chosen for each vortex
    In Section 4.2, the N_f = 2 vortex ansatz uses asymptotic phases exp(i n1 theta) and exp(i n2 theta). These are free topological labels, not fitted values.
assumptions (6)
  • domain assumption Large-N_c QCD restores U_A(1) and makes the eta-prime a light pseudo-Goldstone boson with effective potential (20)
    Standard Witten-Veneziano large-N_c picture; used throughout to justify eta-prime domain walls.
  • domain assumption The eta-prime domain wall hosts an SU(N_c)_{N_f} Chern-Simons theory, dual via level-rank duality to U(N_f)_{-N_c}
    Invoked in Sections 3 and 4 from Refs. [39-42]; foundational for the wall action.
  • ad hoc to paper Level-rank duality with matter, SU(N_c)_{-N_f} + N_f fermions corresponds to U(N_f)_{N_c} + N_f scalars, holds at an assumed nontrivial IR fixed point
    Eq. (28) is the basis for the conjectured Chern-Simons-Higgs theory; the authors admit in Section 6 that it relies on an assumed IR fixed point.
  • ad hoc to paper The Chern-Simons-Higgs Lagrangian L_A (Eq. 30) is the correct effective theory on the eta-prime domain wall
    This is the central conjecture; it is not derived from QCD, only assumed from gauge invariance and minimal coupling.
  • ad hoc to paper Quarks inside a chiral bag can be modeled as condensed Z_{N_c} monopoles
    Section 5.1 proposes this to explain confinement and to source the flux that induces baryon number on the bag surface; no independent evidence is given.
  • domain assumption Cheshire Cat principle: physical observables are independent of the bag radius
    Used in Section 3 to shrink the bag to a vortex line and to identify the Hall droplet with the quark-level description.
invented entities (4)
  • Dual scalar field phi on the eta-prime domain wall
    purpose: Bosonized representation of quarks in the Chern-Simons-Higgs theory; its vortices are baryons
    Introduced in Eqs. (29)-(30) via duality; no direct falsifiable prediction is provided.
  • Emergent U(1) gauge field a on the domain wall
    purpose: Carries the Chern-Simons flux that measures baryon number
    Motivated by level-rank duality and anomaly inflow, but the specific U(1)_{-N_c} theory is conjectural.
  • Confined Z_{N_c} monopoles inside the chiral bag
    purpose: Produce color magnetic flux that induces baryon and color charges on the bag surface
    Proposed in Section 5.1; magnetic monopoles have not been observed, and the Z_{N_c} charge assignment is a modeling assumption.
  • Surface vector meson field V, distinct from the CS gauge field A
    purpose: Carries baryon number outside the bag and cancels the opposite flux of A so that the total baryon number is physical
    Section 5.2 introduces V as a separate surface field; the authors argue A and V cannot be distinguished by location, and no independent check is given.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Baryon Construction with $\eta^\prime$ Meson Field." pith.science (2026). https://pith.science/paper/ZGZK2OBH

@misc{pith2026250118159,
  author       = {Pith},
  title        = {Pith review of: Baryon Construction with $\eta^\prime$ Meson Field},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZGZK2OBH}},
  note         = {Machine review of arXiv:2501.18159}
}
abstract

In the low-energy regime, baryons with $N_f \geq 2$ have long been constructed as skyrmions or through bag models, but such constructions for $N_f = 1$ are hindered by the trivial topological structure of the meson field. Recent proposals suggest that one-flavor baryons can instead be interpreted as quantum Hall droplets on the $\eta'$ domain wall, providing a potential link to quark--hadron continuity at high density. In retrospect, the qualitative or semi-qualitative construction of one-flavor baryons on the $\eta'$ domain wall reveals that these baryons can be described as quantum Hall droplets, resembling topological solitons akin to skyrmions. Using an effective theory on the $\eta'$ domain wall, which is conjectured to be the Chern--Simons--Higgs theory, it is discussed that its vortex solution with unit baryon numbers naturally has a spin of $N_c/2$, and thus can be interpreted as a baryon or multi-baryon structure. The particle--vortex duality suggests that quarks carry a fractional topological charge of $1/N_c$ and obey fractional statistics. In terms of chiral bag models, confinement can be attributed to the monopoles confined within the bag, and the vector meson fields on the bag surface are essential for ensuring the correct baryon number in the chiral bag framework, thereby providing deeper insights into baryons as non-trivial topological structures of the meson field. In this paper, we review the progress in this development, with a special focus on the $\eta^\prime$ domain wall dynamics. Naive extensions to $N_f \geq 2$ are also discussed.

Figures

Figures reproduced from arXiv: 2501.18159 by the authors.

Figure 1
Figure 1. Baryons as quantum Hall droplets and quark-hadron duality. (a) The one-flavor baryon is suggested to be a quantum Hall droplet (picture from [82]). (b) The one-flavor baryon is constructed from the chiral bag model by the Cheshire Cat principle (picture from [44]). The chiral bag construction further clarifies details on baryons as quantum Hall droplets. As mentioned above, the boundary chiral mode is essential, car… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

133 extracted references · 64 canonical work pages

  1. [1]

    Ultraviolet Behavior of Nonabelian Gauge Theories

    Gross, D.J.; Wilczek, F. Ultraviolet Behavior of Nonabelian Gauge Theories. Phys. Rev. Lett. 1973, 30, 1343–1346. https: //doi.org/10.1103/PhysRevLett.30.1343

    doi:10.1103/physrevlett.30.1343 1973

  2. [2]

    Reliable Perturbative Results for Strong Interactions? Phys

    Politzer, H.D. Reliable Perturbative Results for Strong Interactions? Phys. Rev. Lett. 1973, 30, 1346–1349. https://doi.org/10.1103/ PhysRevLett.30.1346

    1973

  3. [3]

    Quantum Chromodynamics: A Review

    Marciano, W.J.; Pagels, H.. Quantum Chromodynamics: A Review. Phys. Rep. 1978, 36, 137. https://doi.org/10.1016/0370-157 3(78)90208-9

    doi:10.1016/0370-157 1978

  4. [4]

    Structure of phenomenological Lagrangians

    Callan, C.G., Jr.; Coleman, S.R.; Wess, J.; Zumino, B. Structure of phenomenological Lagrangians. 2. Phys. Rev. 1969, 177, 2247–2250. https://doi.org/10.1103/PhysRev.177.2247

    doi:10.1103/physrev.177.2247 1969

  5. [5]

    Structure of phenomenological Lagrangians

    Coleman, S.R.; Wess, J.; Zumino, B. Structure of phenomenological Lagrangians. 1. Phys. Rev. 1969, 177, 2239–2247. https: //doi.org/10.1103/PhysRev.177.2239

    doi:10.1103/physrev.177.2239 1969

  6. [6]

    Phenomenological Lagrangians

    Weinberg, S. Phenomenological Lagrangians. Physica A 1979, 96, 327–340. https://doi.org/10.1016/0378-4371(79)90223-1

    doi:10.1016/0378-4371(79)90223-1 1979

  7. [7]

    Chiral Perturbation Theory to One Loop

    Gasser, J.; Leutwyler, H. Chiral Perturbation Theory to One Loop. Ann. Phys. 1984, 158, 142. https://doi.org/10.1016/0003-491 6(84)90242-2

    doi:10.1016/0003-491 1984

  8. [8]

    Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark

    Gasser, J.; Leutwyler, H. Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark. Nucl. Phys. B 1985, 250, 465–516. https://doi.org/10.1016/0550-3213(85)90492-4

    doi:10.1016/0550-3213(85)90492-4 1985

Show all 133 references
  1. [9]

    Nuclear forces from chiral Lagrangians

    Weinberg, S. Nuclear forces from chiral Lagrangians. Phys. Lett. B 1990, 251, 288–292. https://doi.org/10.1016/0370-2693(90)909 38-3

    1990 doi

  2. [10]

    Nucleons with chiral loops

    Gasser, J.; Sainio, M.E.; Svarc, A. Nucleons with chiral loops. Nucl. Phys. B 1988, 307, 779–853. https://doi.org/10.1016/0550-321 3(88)90108-3

    1988 doi

  3. [11]

    QCD phenomenology based on a chiral effective Lagrangian

    Hatsuda, T.; Kunihiro, T. QCD phenomenology based on a chiral effective Lagrangian. Phys. Rep. 1994, 247, 221–367. https: //doi.org/10.1016/0370-1573(94)90022-1

    1994 doi

  4. [13]

    Chiral effective field theory and nuclear forces

    Machleidt, R.; Entem, D.R. Chiral effective field theory and nuclear forces. Phys. Rep. 2011, 503, 1–75. https://doi.org/10.1016/j. physrep.2011.02.001

    2011 doi

  5. [14]

    A Nonlinear field theory

    Skyrme, T.H.R. A Nonlinear field theory. Proc. R. Soc. Lond. A 1961, 260, 127–138. https://doi.org/10.1098/rspa.1961.0018

    1961

  6. [15]

    A Unified Field Theory of Mesons and Baryons

    Skyrme, T.H.R. A Unified Field Theory of Mesons and Baryons. Nucl. Phys. 1962, 31, 556–569. https://doi.org/10.1016/0029-558 2(62)90775-7

    1962 doi

  7. [16]

    The Skyrme Model

    Zahed, I.; Brown, G.E. The Skyrme Model. Phys. Rep. 1986, 142, 1–102. https://doi.org/10.1016/0370-1573(86)90142-0

    1986 doi

  8. [17]

    Baryons in a relativized quark model with chromodynamics

    Capstick, S.; Isgur, N. Baryons in a relativized quark model with chromodynamics. Phys. Rev. D 1986, 34, 2809–2835. https: //doi.org/10.1103/physrevd.34.2809

    1986 doi

  9. [18]

    Baryon Decays in a Quark Model with Chromodynamics

    Koniuk, R.; Isgur, N. Baryon Decays in a Quark Model with Chromodynamics. Phys. Rev. D 1980, 21, 1868. Erratum in Phys. Rev. D 1981, 23, 818. https://doi.org/10.1103/PhysRevD.21.1868

    1980 doi

  10. [19]

    Quark models of baryon masses and decays

    Capstick, S.; Roberts, W. Quark models of baryon masses and decays. Prog. Part. Nucl. Phys. 2000, 45, S241–S331. https: //doi.org/10.1016/S0146-6410(00)00109-5

    2000 doi

  11. [20]

    Lecture notes on the Skyrme model

    Ma, Y.L.; Harada, M. Lecture notes on the Skyrme model. arXiv 2016 , arXiv:1604.04850

    2016 arXiv

  12. [21]

    A Planar Diagram Theory for Strong Interactions

    ’t Hooft, G. A Planar Diagram Theory for Strong Interactions. Nucl. Phys. B 1974, 72, 461. https://doi.org/10.1016/0550-3213(74 )90154-0

    1974 doi

  13. [22]

    Baryons in the 1/n Expansion

    Witten, E. Baryons in the 1/n Expansion. Nucl. Phys. B 1979, 160, 57–115. https://doi.org/10.1016/0550-3213(79)90232-3

    1979 doi

  14. [23]

    Static Properties of Nucleons in the Skyrme Model

    Adkins, G.S.; Nappi, C.R.; Witten, E. Static Properties of Nucleons in the Skyrme Model. Nucl. Phys. B 1983, 228, 552. https://doi.org/10.1016/0550-3213(83)90559-X

    1983 doi

  15. [24]

    Global Aspects of Current Algebra

    Witten, E. Global Aspects of Current Algebra. Nucl. Phys. B 1983, 223, 422–432. https://doi.org/10.1016/0550-3213(83)90063-9

    1983 doi

  16. [25]

    Bosonization Relations as Bag Boundary Conditions

    Nadkarni, S.; Nielsen, H.B.; Zahed, I. Bosonization Relations as Bag Boundary Conditions. Nucl. Phys. B 1985, 253, 308–322. https://doi.org/10.1016/0550-3213(85)90533-4. Symmetry 2025, 1, 0 23 of 27

    1985 doi

  17. [26]

    Nonabelian Cheshire Cat Bag Models in (1+1)-dimensions

    Nadkarni, S.; Zahed, I. Nonabelian Cheshire Cat Bag Models in (1+1)-dimensions. Nucl. Phys. B 1986, 263, 23–36. https: //doi.org/10.1016/0550-3213(86)90025-8

    1986 doi

  18. [27]

    Cheshire cat hadrons

    Rho, M. Cheshire cat hadrons. Phys. Rep. 1994, 240, 1–142. https://doi.org/10.1016/0370-1573(94)90002-7

    1994 doi

  19. [28]

    Color anomaly in a hybrid bag model

    Nielsen, H.B.; Rho, M.; Wirzba, A.; Zahed, I. Color anomaly in a hybrid bag model. Phys. Lett. B 1991, 269, 389–393. https: //doi.org/10.1016/0370-2693(91)90189-W

    1991 doi

  20. [29]

    Topological Soliton Bag Model for Baryons

    Rho, M.; Goldhaber, A.S.; Brown, G.E. Topological Soliton Bag Model for Baryons. Phys. Rev. Lett. 1983, 51, 747–750. https: //doi.org/10.1103/PhysRevLett.51.747

    1983 doi

  21. [31]

    U(1) Without Instantons

    Veneziano, G. U(1) Without Instantons. Nucl. Phys. B 1979, 159, 213–224. https://doi.org/10.1016/0550-3213(79)90332-8

    1979 doi

  22. [32]

    Chiral Dynamics in the Large n Limit.Nucl

    Vecchia, P .D.; Veneziano, G. Chiral Dynamics in the Large n Limit.Nucl. Phys. B 1980, 171, 253–272. https://doi.org/10.1016/05 50-3213(80)90370-3

    1980 doi

  23. [34]

    On the Partial Conservation of the U(1) Current

    Kawarabayashi, K.; Ohta, N. On the Partial Conservation of the U(1) Current. Prog. Theor. Phys. 1981, 66, 1789. https: //doi.org/10.1143/PTP .66.1789

    1981 doi

  24. [35]

    The Problem of η in the Large N Limit: Effective Lagrangian Approach

    Kawarabayashi, K.; Ohta, N. The Problem of η in the Large N Limit: Effective Lagrangian Approach. Nucl. Phys. B 1980, 175, 477–492. https://doi.org/10.1016/0550-3213(80)90024-3

    1980 doi

  25. [36]

    Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions: Topological Structure of Dense Matter

    Ma, Y.L.; Rho, M. Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions: Topological Structure of Dense Matter. Symmetry 2021, 13, 1888. https://doi.org/10.3390/sym13101888

    2021 doi

  26. [37]

    Anomalies of discrete symmetries in three dimensions and group cohomology

    Kapustin, A.; Thorngren, R. Anomalies of discrete symmetries in three dimensions and group cohomology. Phys. Rev. Lett. 2014, 112, 231602. https://doi.org/10.1103/PhysRevLett.112.231602

    2014 doi

  27. [38]

    Coupling a QFT to a TQFT and Duality

    Kapustin, A.; Seiberg, N. Coupling a QFT to a TQFT and Duality. J. High Energy Phys. 2014, 2014 , 1. https://doi.org/10.1007/ JHEP04(2014)001

    2014

  28. [39]

    Generalized Global Symmetries

    Gaiotto, D.; Kapustin, A.; Seiberg, N.; Willett, B. Generalized Global Symmetries. J. High Energy Phys. 2015, 2015 , 172. https://doi.org/10.1007/JHEP02(2015)172

    2015 doi

  29. [40]

    Theta, Time Reversal, and Temperature.J

    Gaiotto, D.; Kapustin, A.; Komargodski, Z.; Seiberg, N. Theta, Time Reversal, and Temperature.J. High Energy Phys. 2017, 2017 ,

    2017

  30. [41]

    Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions

    Gaiotto, D.; Komargodski, Z.; Seiberg, N. Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions. J. High Energy Phys. 2018, 2018 , 110. https://doi.org/10.1007/JHEP01(2018)110

    2018 doi

  31. [42]

    Level/rank Duality and Chern-Simons-Matter Theories

    Hsin, P .S.; Seiberg, N. Level/rank Duality and Chern-Simons-Matter Theories. J. High Energy Phys. 2016, 2016, 95. https: //doi.org/10.1007/JHEP09(2016)095

    2016 doi

  32. [43]

    arXiv 2018, arXiv:1812.09253

    Komargodski, Z.; Baryons as Quantum Hall Droplets. arXiv 2018, arXiv:1812.09253

    2018 arXiv

  33. [44]

    Baryon as a Quantum Hall Droplet and the Cheshire Cat Principle

    Ma, Y.L.; Nowak, M.A.; Rho, M.; Zahed, I. Baryon as a Quantum Hall Droplet and the Cheshire Cat Principle. Phys. Rev. Lett. 2019, 123, 172301. https://doi.org/10.1103/PhysRevLett.123.172301

    2019 doi

  34. [45]

    Towards the hadron–quark continuity via a topology change in compact stars.Prog

    Ma, Y.L.; Rho, M. Towards the hadron–quark continuity via a topology change in compact stars.Prog. Part. Nucl. Phys. 2020, 113, 103791. https://doi.org/10.1016/j.ppnp.2020.103791

    2020

  35. [46]

    Baryons as vortexes on theη’ domain wall

    Lin, F.; Ma, Y.L. Baryons as vortexes on theη’ domain wall. J. High Energy Phys. 2024, 2014 , 270. https://doi.org/10.1007/JHEP0 5(2024)270

    2024 doi

  36. [47]

    An effective field theory model for the fractional quantum hall effect

    Zhang, S.C.; Hansson, T.H.; Kivelson, S. An effective field theory model for the fractional quantum hall effect. Phys. Rev. Lett. 1988, 62, 82–85. https://doi.org/10.1103/PhysRevLett.62.82

    1988 doi

  37. [48]

    A New Extended Model of Hadrons

    Chodos, A.; Jaffe, R.L.; Johnson, K.; Thorn, C.B.; Weisskopf, V .F. A New Extended Model of Hadrons. Phys. Rev. D 1974, 9, 3471–3495. https://doi.org/10.1103/PhysRevD.9.3471

    1974 doi

  38. [49]

    Chiral Symmetry and the Bag Model: A New Starting Point for Nuclear Physics

    Thomas, A.W. Chiral Symmetry and the Bag Model: A New Starting Point for Nuclear Physics. Adv. Nucl. Phys. 1984, 13, 1–137. https://doi.org/10.1007/978-1-4613-9892-9_1

    1984 doi

  39. [50]

    Chiral Hedgehogs in the Bag Theory

    Chodos, A.; Thorn, C.B. Chiral Hedgehogs in the Bag Theory. Phys. Rev. D 1975, 12, 2733. https://doi.org/10.1103/PhysRevD.12 .2733

    1975 doi

  40. [52]

    Dynamically Broken Chiral Symmetry With Bag Confinement

    Goldman, J.T.; Haymaker, R.W. Dynamically Broken Chiral Symmetry With Bag Confinement. Phys. Rev. D 1981, 24, 724. https://doi.org/10.1103/PhysRevD.24.724

    1981 doi

  41. [53]

    Partial Bosonization: The Formalism of Cheshire Cat Bag Models

    Nadkarni, S.; Nielsen, H.B. Partial Bosonization: The Formalism of Cheshire Cat Bag Models. Nucl. Phys. B 1986, 263, 1–22. https://doi.org/10.1016/0550-3213(86)90024-6

    1986 doi

  42. [54]

    Removing Bag Dynamics From Chiral Bag Models: An Illustrative Example

    Perry, R.J.; Rho, M. Removing Bag Dynamics From Chiral Bag Models: An Illustrative Example. Phys. Rev. D 1986, 34, 1169–1175. https://doi.org/10.1103/PhysRevD.34.1169. Symmetry 2025, 1, 0 24 of 27

    1986 doi

  43. [55]

    Smooth bosonization: The Cheshire cat revisited.Nucl

    Damgaard, P .H.; Nielsen, H.B.; Sollacher, R. Smooth bosonization: The Cheshire cat revisited.Nucl. Phys. B 1992, 385, 227–250. https://doi.org/10.1016/0550-3213(92)90100-P

    1992 doi

  44. [56]

    The tale of the eta-prime from the cheshire cat principle

    Nielsen, H.B.; Rho, M.; Wirzba, A.; Zahed, I. The tale of the eta-prime from the cheshire cat principle. Phys. Lett. B 1992, 281, 345–350. https://doi.org/10.1016/0370-2693(92)91153-Z

    1992 doi

  45. [57]

    Confined Monopoles in Chiral Bag

    Lin, F.; Ma, Y.L. Confined Monopoles in Chiral Bag. arXiv 2025, arXiv:2501.16653

    2025 arXiv

  46. [58]

    Consequences of anomalous Ward identities

    Wess, J.; Zumino, B. Consequences of anomalous Ward identities. Phys. Lett. B 1971, 37, 95–97. https://doi.org/10.1016/0370-269 3(71)90582-X

    1971 doi

  47. [59]

    From Skyrmions to One Flavored Baryons and Beyond

    Karasik, A. From Skyrmions to One Flavored Baryons and Beyond. Symmetry 2022, 14, 2347. https://doi.org/10.3390/sym14112 347

    2022 doi

  48. [60]

    Fermion Number Fractionization in Quantum Field Theory

    Niemi, A.J.; Semenoff, G.W. Fermion Number Fractionization in Quantum Field Theory. Phys. Rep. 1986, 135, 99. https: //doi.org/10.1016/0370-1573(86)90167-5

    1986 doi

  49. [61]

    Skyrmions and the alpha-particle model of nuclei.Proc

    Battye, R.; Manton, N.S.; Sutcliffe, P . Skyrmions and the alpha-particle model of nuclei.Proc. R. Soc. Lond. A 2007, 463, 261–279. https://doi.org/10.1098/rspa.2006.1767

    2007

  50. [62]

    Skyrmion approach to finite density and temperature.arXiv 2009, arXiv:0906.3263

    Park, B.Y.; Vento, V . Skyrmion approach to finite density and temperature.arXiv 2009, arXiv:0906.3263. https://doi.org/10.1142/ 9789814280709_0005

    2009 arXiv

  51. [63]

    The Multifaceted Skyrmion; World Scientific: Singapore, 2010; ISBN 978-981-4280-69-3; 978-981-4467-16-2

    Brown, G.E.; Rho, M. The Multifaceted Skyrmion; World Scientific: Singapore, 2010; ISBN 978-981-4280-69-3; 978-981-4467-16-2. https://doi.org/10.1142/7397

    2010 doi

  52. [64]

    Recent progress on dense nuclear matter in skyrmion approaches

    Ma, Y.L.; Rho, M. Recent progress on dense nuclear matter in skyrmion approaches. Sci. China Phys. Mech. Astron. 2017, 60, 032001. https://doi.org/10.1007/s11433-016-0497-2

    2017 doi

  53. [65]

    Skyrmions and clustering in light nuclei

    Naya, C.; Sutcliffe, P . Skyrmions and clustering in light nuclei. Phys. Rev. Lett. 2018, 121, 232002. https://doi.org/10.1103/ PhysRevLett.121.232002

    2018

  54. [66]

    Skyrmions—A Theory of Nuclei ; World Scientific: Singapore, 2022; ISBN 978-1-80061-247-1; 978-1-80061-249-5

    Manton, N.S. Skyrmions—A Theory of Nuclei ; World Scientific: Singapore, 2022; ISBN 978-1-80061-247-1; 978-1-80061-249-5. https://doi.org/10.1142/q0368

    2022 doi

  55. [67]

    Vector meson effects on multi-Skyrmion states from the rational map ansatz.Sci

    Wang, J.S.; Ma, Y.L. Vector meson effects on multi-Skyrmion states from the rational map ansatz.Sci. China Phys. Mech. Astron. 2023, 66, 112011. https://doi.org/10.1007/s11433-023-2220-y

    2023 doi

  56. [68]

    A New Skyrmion Crystal

    Kugler, M.; Shtrikman, S. A New Skyrmion Crystal. Phys. Lett. B 1988, 208, 491–494. https://doi.org/10.1016/0370-2693(88)906 53-3

    1988 doi

  57. [69]

    Skyrmion Crystals and Their Symmetries

    Kugler, M.; Shtrikman, S. Skyrmion Crystals and Their Symmetries. Phys. Rev. D 1989, 40, 3421. https://doi.org/10.1103/ PhysRevD.40.3421

    1989

  58. [70]

    Maximal Symmetry of the Skyrme Crystal

    Goldhaber, A.S.; Manton, N.S. Maximal Symmetry of the Skyrme Crystal. Phys. Lett. B 1987, 198, 231–234. https://doi.org/10.101 6/0370-2693(87)91502-4

    1987

  59. [71]

    Sliding vacua in dense skyrmion matter

    Lee, H.J.; Park, B.Y.; Rho, M.; Vento, V . Sliding vacua in dense skyrmion matter. Nucl. Phys. A 2003, 726, 69–92. https: //doi.org/10.1016/S0375-9474(03)01626-9

    2003 doi

  60. [72]

    Half-Skyrmions, Tensor Forces and Symmetry Energy in Cold Dense Matter.Phys

    Lee, H.K.; Park, B.Y.; Rho, M. Half-Skyrmions, Tensor Forces and Symmetry Energy in Cold Dense Matter.Phys. Rev. C 2011, 83, 025206. Erratum in Phys. Rev. C 2011, 84, 059902. https://doi.org/10.1103/PhysRevC.84.059902

    2011 doi

  61. [73]

    Shell model description of the C-14 dating beta decay with Brown-Rho-scaled NN interactions

    Holt, J.W.; Brown, G.E.; Kuo, T.T.S.; Holt, J.D.; Machleidt, R. Shell model description of the C-14 dating beta decay with Brown-Rho-scaled NN interactions. Phys. Rev. Lett. 2008, 100, 062501. https://doi.org/10.1103/PhysRevLett.100.062501

    2008 doi

  62. [74]

    Scale-Invariant Hidden Local Symmetry, Topology Change and Dense Baryonic Matter

    Paeng, W.G.; Kuo, T.T.S.; Lee, H.K.; Rho, M. Scale-Invariant Hidden Local Symmetry, Topology Change and Dense Baryonic Matter. Phys. Rev. C 2016, 93, 055203. https://doi.org/10.1103/PhysRevC.93.055203

    2016 doi

  63. [75]

    Scale-invariant hidden local symmetry, topology change, and dense baryonic matter

    Paeng, W.G.; Kuo, T.T.S.; Lee, H.K.; Ma, Y.L.; Rho, M. Scale-invariant hidden local symmetry, topology change, and dense baryonic matter. II. Phys. Rev. D 2017, 96, 014031. https://doi.org/10.1103/PhysRevD.96.014031

    2017 doi

  64. [76]

    Pseudoconformal equation of state in compact-star matter from topology change and hidden symmetries of QCD

    Ma, Y.L.; Lee, H.K.; Paeng, W.G.; Rho, M. Pseudoconformal equation of state in compact-star matter from topology change and hidden symmetries of QCD. Sci. China Phys. Mech. Astron. 2019, 62, 112011. https://doi.org/10.1007/s11433-019-9399-5

    2019 doi

  65. [77]

    Chiral bag model for the nucleon

    Hosaka, A.; Toki, H. Chiral bag model for the nucleon. Phys. Rep. 1996, 277, 65–188. https://doi.org/10.1016/S0370-1573(96)000 13-0

    1996 doi

  66. [78]

    Fractional Quantum Numbers on Solitons

    Goldstone, J.; Wilczek, F. Fractional Quantum Numbers on Solitons. Phys. Rev. Lett. 1981, 47, 986–989. https://doi.org/10.1103/ PhysRevLett.47.986

    1981

  67. [79]

    On the Vacuum Baryon Number in the Chiral Bag Model

    Jaroszewicz, T. On the Vacuum Baryon Number in the Chiral Bag Model. Phys. Lett. B 1984, 143, 217–221. https://doi.org/10.101 6/0370-2693(84)90838-4

    1984

  68. [80]

    Skyrmions and Fractional Quantum Hall Droplets Unified by Hidden Symmetries in Dense Matter

    Rho, M. Skyrmions and Fractional Quantum Hall Droplets Unified by Hidden Symmetries in Dense Matter. arXiv 2021, arXiv:2109.10059

    2021 arXiv

  69. [81]

    Vector dominance, one flavored baryons, and QCD domain walls from the “hidden” Wess-Zumino term

    Karasik, A. Vector dominance, one flavored baryons, and QCD domain walls from the “hidden” Wess-Zumino term. SciPost Phys. 2021, 10, 138. https://doi.org/10.21468/SciPostPhys.10.6.138

    2021 doi

  70. [82]

    Skyrmions, Quantum Hall Droplets, and one current to rule them all

    Karasik, A. Skyrmions, Quantum Hall Droplets, and one current to rule them all. SciPost Phys. 2020, 9, 8. https://doi.org/10.214 68/SciPostPhys.9.1.008. Symmetry 2025, 1, 0 25 of 27

    2020

  71. [83]

    Symmetry Breaking Through Bell-Jackiw Anomalies

    ’t Hooft, G. Symmetry Breaking Through Bell-Jackiw Anomalies. Phys. Rev. Lett. 1976, 37, 8–11. https://doi.org/10.1103/ PhysRevLett.37.8

    1976

  72. [84]

    How Instantons Solve the U(1) Problem.Phys

    ’t Hooft, G. How Instantons Solve the U(1) Problem.Phys. Rep. 1986, 142, 357–387. https://doi.org/10.1016/0370-1573(86)90117-1

    1986 doi

  73. [85]

    Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2-D qYM theory.J

    Naculich, S.G.; Schnitzer, H.J. Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2-D qYM theory.J. High Energy Phys. 2007, 2007 , 23. https://doi.org/10.1088/1126-6708/2007/06/023. [arXiv:hep-th/0703089 [hep-th]]

    2007 arXiv

  74. [86]

    Level rank duality of WZW models in conformal field theory.Commun

    Nakanishi, T.; Tsuchiya, A. Level rank duality of WZW models in conformal field theory.Commun. Math. Phys. 1992, 144, 351–372. https://doi.org/10.1007/BF02101097

    1992 doi

  75. [87]

    Baryons, monopoles and dualities in Chern-Simons-matter theories

    Aharony, O. Baryons, monopoles and dualities in Chern-Simons-matter theories. J. High Energy Phys. 2016, 2016 , 93. https: //doi.org/10.1007/JHEP02(2016)093

    2016 doi

  76. [88]

    Group Level Duality in WZW Models and Chern-Simons Theory.Phys

    Naculich, S.G.; Riggs, H.A.; Schnitzer, H.J. Group Level Duality in WZW Models and Chern-Simons Theory.Phys. Lett. B 1990, 246, 417–422. https://doi.org/10.1016/0370-2693(90)90623-E

    1990 doi

  77. [89]

    The Large N Limit of Chern-Simons Gauge Theory

    Camperi, M.; Levstein, F.; Zemba, G. The Large N Limit of Chern-Simons Gauge Theory. Phys. Lett. B 1990, 247, 549–554. https://doi.org/10.1016/0370-2693(90)91899-M. https://doi.org/10.1016/0550-3213(91)90110-J

    1990 doi

  78. [90]

    Anomalous Baryon Number in (1+1)-Dimensions

    Zahed, I. Anomalous Baryon Number in (1+1)-Dimensions. Phys. Rev. D 1984, 30, 2221–2226. https://doi.org/10.1103/PhysRevD. 30.2221

    1984 doi

  79. [91]

    https://doi.org/10.1007/JHEP05(2017)091

    2017 doi

  80. [92]

    Anomalies and Fermion Zero Modes on Strings and Domain Walls

    Callan, C.G.; Jr; Harvey, J.A. Anomalies and Fermion Zero Modes on Strings and Domain Walls. Nucl. Phys. B 1985, 250, 427–436. https://doi.org/10.1016/0550-3213(85)90489-4

    1985 doi

  81. [93]

    Peculiar Charged Vortices in Higgs Models With Pure Chern-Simons Term.Phys

    Jatkar, D.P .; Khare, A. Peculiar Charged Vortices in Higgs Models With Pure Chern-Simons Term.Phys. Lett. B 1990, 236, 283–286. https://doi.org/10.1016/0370-2693(90)90983-D

    1990 doi

  82. [94]

    Magnetic Flux, Angular Momentum, and Statistics

    Wilczek, F. Magnetic Flux, Angular Momentum, and Statistics. Phys. Rev. Lett. 1982, 48, 1144–1146. https://doi.org/10.1103/ PhysRevLett.48.1144

    1982

  83. [95]

    An Anyon primer

    Rao, S. An Anyon primer. arXiv 1992, arXiv:hep-th/9209066

    1992 arXiv

  84. [96]

    Exotic Baryon NumberB = 2 States in the SU(2) Skyrme Model

    Weigel, H.; Schwesinger, B.; Holzwarth, G. Exotic Baryon NumberB = 2 States in the SU(2) Skyrme Model. Phys. Lett. B 1986, 168, 321–325. https://doi.org/10.1016/0370-2693(86)91637-0

    1986 doi

  85. [97]

    Rational maps, monopoles and Skyrmions

    Houghton, C.J.; Manton, N.S.; Sutcliffe, P .M. Rational maps, monopoles and Skyrmions. Nucl. Phys. B 1998, 510, 507–537. https://doi.org/10.1016/S0550-3213(97)00619-6

    1998 doi

  86. [98]

    Mandelstam ’t Hooft Duality in Abelian Lattice Models

    Peskin, M.E. Mandelstam ’t Hooft Duality in Abelian Lattice Models. Ann. Phys. 1978, 113, 122. https://doi.org/10.1016/0003-4 916(78)90252-X

    1978 doi

  87. [99]

    Lectures on the Quantum Hall Effect

    Tong, D. Lectures on the Quantum Hall Effect. arXiv 2016, arXiv:1606.06687

    2016 arXiv

  88. [100]

    M. Eto, K. Nishimura and M. Nitta, Domain-wall Skyrmion phase in a rapidly rotating QCD matter. J. High Energy Phys. 2024, 2024 , 19. https://doi.org/10.1007/JHEP03(2024)019

    2024 doi

  89. [101]

    Non-Abelian chiral soliton lattice in rotating QCD matter: Nambu-Goldstone and excited modes

    Eto, M.; Nishimura, K.; Nitta, M. Non-Abelian chiral soliton lattice in rotating QCD matter: Nambu-Goldstone and excited modes. J. High Energy Phys. 2024, 2024 , 35. https://doi.org/10.1007/JHEP03(2024)035

    2024 doi

  90. [102]

    Mesons, baryons and waves in the baby Skyrmion model.Eur

    Kudryavtsev, A.E.; Piette, B.; Zakrzewski, W.J. Mesons, baryons and waves in the baby Skyrmion model.Eur. Phys. J. C 1998, 1, 333–341 https://doi.org/10.1007/BF01245822

    1998 doi

  91. [103]

    Isospinning baby Skyrmion solutions

    Battye, R.A.; Haberichter, M. Isospinning baby Skyrmion solutions. Phys. Rev. D 2013, 88, 125016. https://doi.org/10.1103/ PhysRevD.88.125016

    2013

  92. [104]

    Skyrmion and Baby Skyrmion Formation from Domain Walls

    Winyard, T. Skyrmion and Baby Skyrmion Formation from Domain Walls. arXiv 2015, arXiv:1507.07482

    2015 arXiv

  93. [105]

    Baby skyrmion crystals stabilized by vector mesons.Phys

    Leask, P . Baby skyrmion crystals stabilized by vector mesons.Phys. Lett. B 2024, 855, 138842. https://doi.org/10.1016/j.physletb. 2024.138842

    2024

  94. [106]

    Hall Droplet Sheets in Holographic QCD

    Bigazzi, F.; Cotrone, A.L.; Olzi, A. Hall Droplet Sheets in Holographic QCD. J. High Energy Phys. 2023, 2023 , 194. https: //doi.org/10.1007/JHEP02(2023)194

    2023 doi

  95. [107]

    Anomalous effects of dense matter under rotation

    Huang, X.G.; Nishimura, K.; Yamamoto, N. Anomalous effects of dense matter under rotation. J. High Energy Phys. 2018, 2018 , 69. https://doi.org/10.1007/JHEP02(2018)069

    2018 doi

  96. [108]

    Anomaly-Induced Effects of Rotating Dense Matter

    Huang, X.G.; Nishimura, K.; Yamamoto, N. Anomaly-Induced Effects of Rotating Dense Matter. JPS Conf. Proc. 2019, 26, 031020. https://doi.org/10.7566/JPSCP .26.031020

    2019 doi

  97. [109]

    Topological term, QCD anomaly, and theη ′ chiral soliton lattice in rotating baryonic matter

    Nishimura, K.; Yamamoto, N. Topological term, QCD anomaly, and theη ′ chiral soliton lattice in rotating baryonic matter. J. High Energy Phys. 2020, 2020 , 196. https://doi.org/10.1007/JHEP07(2020)196

    2020 doi

  98. [110]

    Phases of rotating baryonic matter: non-Abelian chiral soliton lattices, antiferro-isospin chains, and ferri/ferromagnetic magnetization

    Eto, M.; Nishimura, K.; Nitta, M. Phases of rotating baryonic matter: non-Abelian chiral soliton lattices, antiferro-isospin chains, and ferri/ferromagnetic magnetization. J. High Energy Phys. 2022, 2022 , 305. https://doi.org/10.1007/JHEP08(2022)305

    2022 doi

  99. [111]

    Correspondence between Skyrmions in 2+1 and 3+1 Dimensions

    Nitta, M. Correspondence between Skyrmions in 2+1 and 3+1 Dimensions. Phys. Rev. D 2013, 87, 025013. https://doi.org/10.110 3/PhysRevD.87.025013

    2013

  100. [112]

    Non-Abelian Sine-Gordon Solitons: Correspondence between SU(N) Skyrmions and CPN−1 Lumps

    Eto, M.; Nitta, M. Non-Abelian Sine-Gordon Solitons: Correspondence between SU(N) Skyrmions and CPN−1 Lumps. Phys. Rev. D 2015, 91, 085044. https://doi.org/10.1103/PhysRevD.91.085044

    2015 doi

  101. [113]

    Relations among topological solitons

    Nitta, M. Relations among topological solitons. Phys. Rev. D 2022, 105, 105006. https://doi.org/10.1103/PhysRevD.105.105006. Symmetry 2025, 1, 0 26 of 27

    2022 doi

  102. [114]

    Domain wall Skyrmions

    Gudnason, S.B.; Nitta, M. Domain wall Skyrmions. Phys. Rev. D 2014, 89, 085022. https://doi.org/10.1103/PhysRevD.89.085022

    2014 doi

  103. [115]

    How baryons appear in low-energy QCD: Domain-wall Skyrmion phase in strong magnetic fields

    Eto, M.; Nishimura, K.; Nitta, M. How baryons appear in low-energy QCD: Domain-wall Skyrmion phase in strong magnetic fields. arXiv 2023, arXiv:2304.02940

    2023 arXiv

  104. [116]

    Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice

    Eto, M.; Nishimura, K.; Nitta, M. Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice. J. High Energy Phys. 2023, 2023 , 32. https://doi.org/10.1007/JHEP12(2023)032

    2023 doi

  105. [117]

    Baryonic Vortex Phase and Magnetic Field Generation in QCD with Isospin and Baryon Chemical Potentials

    Qiu, Z.; Nitta, M. Baryonic Vortex Phase and Magnetic Field Generation in QCD with Isospin and Baryon Chemical Potentials. arXiv 2024, arXiv:2403.07433

    2024 arXiv

  106. [118]

    Skyrmions in a magnetic field and π0 domain wall formation in dense nuclear matter

    Chen, S.; Fukushima, K.; Qiu, Z. Skyrmions in a magnetic field and π0 domain wall formation in dense nuclear matter. Phys. Rev. D 2022, 105, L011502. https://doi.org/10.1103/PhysRevD.105.L011502

    2022 doi

  107. [119]

    Anomaly inflow on QCD axial domain-walls and vortices

    Fukushima, K.; Imaki, S. Anomaly inflow on QCD axial domain-walls and vortices. Phys. Rev. D 2018, 97, 114003. https: //doi.org/10.1103/PhysRevD.97.114003

    2018 doi

  108. [120]

    Topological Model for Domain Walls in (Super-)Yang-Mills Theories

    Dierigl, M.; Pritzel, A. Topological Model for Domain Walls in (Super-)Yang-Mills Theories. Phys. Rev. D 2014, 90, 105008. https://doi.org/10.1103/PhysRevD.90.105008

    2014 doi

  109. [121]

    Symmetries and Strings in Field Theory and Gravity

    Banks, T.; Seiberg, N. Symmetries and Strings in Field Theory and Gravity. Phys. Rev. D 2011, 83, 084019. https://doi.org/10.110 3/PhysRevD.83.084019

    2011

  110. [122]

    Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories.arXiv 2013, arXiv:1307.4793

    Gukov, S.; Kapustin, A. Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories.arXiv 2013, arXiv:1307.4793

    2013 arXiv

  111. [123]

    Exactly Soluble Diffeomorphism Invariant Theories

    Horowitz, G.T. Exactly Soluble Diffeomorphism Invariant Theories. Commun. Math. Phys. 1989, 125, 417. https://doi.org/10.100 7/BF01218410

    1989

  112. [124]

    Vector mesons on the wall.J

    Kitano, R.; Matsudo, R. Vector mesons on the wall.J. High Energy Phys. 2021, 2021 , 23. https://doi.org/10.1007/JHEP03(2021)023

    2021 doi

  113. [125]

    Dyons of Charge e theta/2 pi

    Witten, E. Dyons of Charge e theta/2 pi. Phys. Lett. B 1979, 86, 283–287/ https://doi.org/10.1016/0370-2693(79)90838-4

    1979 doi

  114. [126]

    Hidden local symmetry at one loop

    Harada, M.; Yamawaki, K. Hidden local symmetry at one loop. Phys. Lett. B 1992, 297, 151–158. https://doi.org/10.1016/0370-2 693(92)91084-M

    1992 doi

  115. [127]

    Hidden local symmetry at loop: A New perspective of composite gauge boson and chiral phase transition

    Harada, M.; Yamawaki, K. Hidden local symmetry at loop: A New perspective of composite gauge boson and chiral phase transition. Phys. Rep. 2003, 381, 1–233. https://doi.org/10.1016/S0370-1573(03)00139-X

    2003 doi

  116. [128]

    Is rho Meson a Dynamical Gauge Boson of Hidden Local Symmetry? Phys

    Bando, M.; Kugo, T.; Uehara, S.; Yamawaki, K.; Yanagida, T. Is rho Meson a Dynamical Gauge Boson of Hidden Local Symmetry? Phys. Rev. Lett. 1985, 54, 1215. https://doi.org/10.1103/PhysRevLett.54.1215

    1985 doi

  117. [129]

    Nonlinear Realization and Hidden Local Symmetries

    Bando, M.; Kugo, T.; Yamawaki, K. Nonlinear Realization and Hidden Local Symmetries. Phys. Rep. 1988, 164, 217–314. https://doi.org/10.1016/0370-1573(88)90019-1

    1988 doi

  118. [130]

    The Baryon Number in Chiral Bag Models

    Goldstone, J.; Jaffe, R.L. The Baryon Number in Chiral Bag Models. Phys. Rev. Lett. 1983, 51, 1518. https://doi.org/10.1103/ PhysRevLett.51.1518

    1983

  119. [131]

    The Spin of the Proton in a Hybrid Chiral Bag Model

    Dreiner, H.K.; Ellis, J.R.; Flores, R.A. The Spin of the Proton in a Hybrid Chiral Bag Model. Phys. Lett. B 1989, 221, 167–172. https://doi.org/10.1016/0370-2693(89)91492-5

    1989 doi

  120. [132]

    Crewther, R.J.; Tunstall, L.C.∆I = 1/2 rule for kaon decays derived from QCD infrared fixed point. Phys. Rev. D 2015, 91, 034016. https://doi.org/10.1103/PhysRevD.91.034016

    2015 doi

  121. [133]

    Chiral-scale effective theory including a dilatonic meson

    Li, Y.L.; Ma, Y.L.; Rho, M. Chiral-scale effective theory including a dilatonic meson. Phys. Rev. D 2017, 95, 114011. https: //doi.org/10.1103/PhysRevD.95.114011

    2017 doi

  122. [134]

    Vector manifestation of the chiral symmetry.Phys

    Harada, M.; Yamawaki, K. Vector manifestation of the chiral symmetry.Phys. Rev. Lett. 2001, 86, 757–760. https://doi.org/10.110 3/PhysRevLett.86.757

    2001

  123. [135]

    Fate of vector dominance in the effective field theory

    Harada, M.; Yamawaki, K. Fate of vector dominance in the effective field theory. Phys. Rev. Lett. 2001, 87, 152001. https: //doi.org/10.1103/PhysRevLett.87.152001. Symmetry 2025, 1, 0 27 of 27

    2001 doi

  124. [136]

    Vector Realization of Chiral Symmetry.Nucl

    Georgi, H. Vector Realization of Chiral Symmetry.Nucl. Phys. B 1990, 331, 311–330. https://doi.org/10.1016/0550-3213(90)90210 -5

    1990 doi

  125. [137]

    Topology and Emergent Symmetries in Dense Compact Star Matter

    Ma, Y.L.; Yang, W.C. Topology and Emergent Symmetries in Dense Compact Star Matter. Symmetry 2023, 15, 776. https: //doi.org/10.3390/sym15030776. Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual aut...

    2023 doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.