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REVIEW 2 major objections 4 minor 87 references

Cosmic strings and domain walls of the QCD quark condensate with and without a hidden axion

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper argues that QCD's quark condensate can form cosmic string-wall defects on its own, without any hidden axion, and that these defects may dominate early-universe cosmology.

desk verdict A coherent EFT analysis with one new, checkable claim about axion-string zero modes and one load-bearing extrapolation about pure-QCD eta-prime walls that needs external support. read the letter →

arxiv 2505.03542 v1 pith:NEKFSL6S submitted 2025-05-06 hep-ph astro-ph.COhep-th

Gia Dvali , Lucy Komisel , Anja Stuhlfauth This is my paper · ORCID
classification hep-phastro-ph.COhep-th
keywords cosmicstringsdomainwallsquarkcondensateaxioneta-primemesonneutralpionstrongCPproblemanomalyinflow
topics The Strong CP Problem
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 tries to establish that the phase of the QCD quark condensate supports topologically nontrivial winding configurations: 2π domain walls bounded by cosmic strings, in the flavor directions of the η′ meson and the neutral pion π0. These string-wall systems exist in pure QCD, independently of any Peccei-Quinn axion, because the η′ itself acts as a poor-quality axion coupled to the QCD θ-vacuum. When a hidden axion does exist, the energetically preferred string winds the quark-condensate phase oppositely to the axion phase, making the string's fermion zero modes anomaly-free rather than superconducting. The paper further argues that, if the QCD scale was larger during or after inflation, these condensate string-walls could be the main drivers of early θ-vacuum cosmology, producing gravitational waves and electromagnetic radiation as they collapse.

What carries the argument

The central machinery is the effective Lagrangian for the phase degrees of freedom $\theta_\phi$ (the Peccei-Quinn phase) and $\theta_\eta$ (the quark-condensate phase), with kinetic terms $f_\phi^2(\partial\theta_\phi)^2 + f_\eta^2(\partial\theta_\eta)^2$ and a cosine potential $\Lambda^4 \cos(\theta_\phi + \theta_\eta - \bar\theta) + \Lambda^4_m \cos(\theta_\eta)$ that encodes instanton effects and quark masses. The instanton-induced cosine correlates the two windings, forcing the phases to wind oppositely around the minimal string ($\theta_\phi = -\theta_\eta$), and the energy functional decides whether the string is free of or attached to a domain wall. The wall profile is the Sine-Gordon solution $4\arctan(e^{m l})$. For the pure-QCD η′ wall, the paper imports assurance from large-$N$ supersymmetric Yang-Mills domain-wall solutions, where the gaugino condensate stays nonzero across the wall, to argue that the quark-condensate phase remains well-defined across the QCD wall.

What would settle it

A lattice QCD computation of the chiral condensate in a background with the effective θ-angle varying by 2π: if the condensate magnitude $|\langle \bar\psi\psi\rangle|$ dips to zero inside the wall, or the phase does not wind by exactly 2π, the pure-QCD η′ string-wall system does not exist as claimed.

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Extended reading notes

Core claim

The central claim is that the chiral quark condensate of QCD, whose phase is the dynamical degree of freedom for the η′ meson, supports 2π-winding domain walls bounded by cosmic strings in two flavor directions. In the η′ direction, the phases of light-quark condensates wind with the same sign; in the π0 direction, they wind oppositely ($n_{\theta_u} = -n_{\theta_d}$). These defects arise in pure QCD, without a hidden axion, because the η′ meson is an axion-like field that cancels the θ-angle in the massless-quark limit, albeit with poor quality once quark masses are included. In hidden-axion theories, the paper shows that the minimal string winds the quark-condensate phase in the opposite sense to the Peccei-Quinn phase, so the localized fermion zero modes have opposite chiralities and the string is anomaly-free. The paper also argues that early-universe scenarios with an enhanced QCD scale can make η′ and pion string-wall systems cosmologically dominant, even when a Peccei-Quinn axion is present.

Load-bearing premise

For a pure-QCD η′ wall to be a genuine 2π phase winding, the magnitude of the quark condensate must stay nonzero through the wall so that the phase is defined at every point except the string core.

Editorial extensions

If this is right

  • Pure QCD supports at least two types of string-wall systems with 2π windings in the η′ and π0 directions, independent of any axion, which can form during the QCD phase transition and later collapse into hadrons, electromagnetic radiation, and gravitational waves.
  • In theories with a Peccei-Quinn axion, the minimal string winds the quark-condensate phase opposite to the axion phase, so the string's fermion zero-mode set is anomaly free; such strings are not superconducting in the original Witten sense.
  • If the QCD scale was larger during or soon after inflation, the hierarchy $f_\phi/\Lambda$ can invert, making η′ and pion string-wall systems the dominant θ-defects of early cosmology rather than hidden-axion strings.
  • In DFSZ-type axion models, winding of the Peccei-Quinn and Higgs phases is generically accompanied by pion-winding of the quark condensate, and such strings can carry Z-boson magnetic flux; in an early-strong-QCD epoch, pion strings may be local strings with integer flux.
  • From the low-energy meson theory, these string-wall systems are solitonic states whose production in heavy-ion collisions requires overcoming an exponential suppression, a possibility that deserves further quantitative study.

Reading between the lines

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

  • If pure-QCD η′ string-wall networks exist, they could act as a foreground or even a dominant source for gravitational-wave and electromagnetic signals currently attributed to axion strings, so observational searches for axion cosmic strings may need to model QCD-condensate defects as well.
  • The anomaly-free nature of the minimal string suggests that the superconducting-string bounds derived from charged zero modes on axionic strings may not apply to the lowest-energy string configurations in KSVZ-type models, potentially relaxing some astrophysical constraints.
  • A lattice QCD computation of the η′ string-wall profile, measuring the condensate magnitude $|\langle \bar\psi\psi\rangle|$ and phase winding across the wall, would directly test whether the large-$N$ supersymmetric extrapolation survives in real QCD.
  • The same phase-winding mechanism may apply to other fermion condensates in the Standard Model and beyond, such as neutrino condensates or the proposed electroweak $\eta_w$ meson, suggesting a general class of string-wall defects from anomalous condensates.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper argues that the phase of the QCD chiral quark condensate can wind by 2π in the η′ or π0 flavor directions, producing metastable domain walls bounded by cosmic strings even in the absence of a Peccei-Quinn axion. In KSVZ-like models the minimal axionic string winds the light-quark condensate phase opposite to the PQ phase, so the light-quark zero mode generated through the effective 't Hooft Yukawa coupling has opposite chirality to the heavy-quark zero mode, making the string world-sheet anomaly-free. The same logic is extended to DFSZ-like models, and the paper discusses cosmological consequences of QCD-condensate string-wall systems, including scenarios with an early strong-QCD epoch, as well as possible heavy-ion signatures. The analytical core is an effective Lagrangian for the phase degrees of freedom; the Appendix explicitly minimizes a variational energy functional to compare string-wall regimes.

Significance. If the central claims hold, this is a significant conceptual shift: pure QCD would support η′ and π0 string-wall networks, and axionic strings would generically be anomaly-free with altered superconducting and astrophysical signatures. The paper's analytical core is internally coherent: the Appendix's minimization of Eq. (89) is explicit, the regime comparison in Eq. (95) supports the opposite-winding string, and the zero-mode chirality argument via the effective Yukawa coupling of Eq. (47) is self-consistent. The main caveat is that the pure-QCD η′ wall requires the condensate modulus to remain nonzero through the wall, a point that is not established within the effective theory and is instead imported from a supersymmetric large-N analogy.

major comments (2)
  1. [VIII] The existence of the pure-QCD η′ 2π-wall as a phase-winding object requires |⟨q̄q⟩| ≠ 0 everywhere except the string core, since otherwise θη is undefined inside the wall. Section VIII explicitly concedes that 'within the wall the effective theory of the order parameter breaks down', and the only support offered is an extrapolation from large-N N=1 SYM domain walls: 'Extrapolating this result to our case of ordinary QCD with quarks in the fundamental representation, we get the assurance that η′ remains well-defined across the wall.' This is an analogy, not a derivation: the SYM wall is BPS and interpolates between distinct vacua of a spontaneously broken discrete symmetry, whereas the η′ wall is non-BPS, connects identical vacua, and has m_η′ ~ Λ, so there is no scale separation protecting the radial mode. The claim in Section XII that the structures are 'fully supported by numerical results' in [22] is not verifiable because [22] is listed as 'in progress'. This is load-bearing for the pure-QCD central claim; please either supply an independent computation, such as a lattice or a controlled model calculation of the condensate profile, or explicitly present the existence claim as conditional on this assumption.
  2. [VIII (π0 paragraph)] The pure-QCD π0 string-wall claim has the same modulus issue as the η′ wall, but the paper asserts without demonstration that 'the analogous question does not arise for domain walls with π0 winding.' Since a π0 winding corresponds to θu = −θd in the two condensate phases, a vanishing of the radial mode in either condensate would again make the phase ill-defined. Please provide the argument that the phase remains well-defined through the pion wall, or qualify the claim accordingly.
minor comments (4)
  1. [X and reference [66]] The text refers to 'RIHC'; this should be 'RHIC'.
  2. [IX] In the sentence 'the PQ field could could have been in the symmetric vacuum', the word 'could' is duplicated.
  3. [Appendix, Eq. (89)] The expression for σ(Lϕ, Lη) contains a factor 1/(Lϕ − Lη) and is singular at Lϕ = Lη; the limiting form used to obtain Eq. (90) should be stated explicitly, since the Lϕ = Lη regime is the one that is minimized.
  4. [Figure 1 caption] The caption states that the linear-ansatz behavior is 'confirmed by numerical analysis [22]', but [22] is unpublished; please either remove this attribution or describe the numerical method and results in the manuscript.

Circularity Check

1 steps flagged · score 4.0 of 10

The effective-Lagrangian derivations are self-contained; the one load-bearing external premise, that the pure-QCD η′ condensate phase stays well defined inside the 2π wall, is imported by extrapolation from the authors' own large-N supersymmetric domain-wall papers.

  1. self citation load bearing [Section VIII ('Internal structure of QCD walls'), discussion of whether the quark condensate remains non-zero across the η′ wall]
    "an immediate technical obstacle for resolving the internal structure of the pure-QCD η′ domain wall is that within the wall the effective theory of the order parameter breaks down. However, we are not interested in an exact solution but only in an assurance that the condensate is non-zero across the wall. ... Extrapolating this result to our case of ordinary QCD with quarks in the fundamental representation, we get the assurance that η′ remains well-defined across the wall."

    The pure-QCD η′ 2π-wall is characterized as a 2π winding of the quark-condensate phase, which is well defined only if |⟨q̄q⟩| stays non-zero through the wall. The paper concedes that inside the wall the effective theory of the order parameter breaks down, so this existence condition is not derived from the Lagrangians of Sections IV–VI. The only assurance offered is an extrapolation from domain-wall solutions in N=1 large-N supersymmetric Yang-Mills (Refs. [35],[37]), which are prior works by the present authors and concern the adjoint gaugino condensate, not QCD with fundamental quarks. Thus the load-bearing premise 'η′ remains well-defined across the wall' reduces for present purposes to a self-citation plus an asserted analogy rather than to a computation from the paper's stated inputs.

full rationale

The derivation chain is largely self-contained: the effective Lagrangians for θφ and θη, the sine-Gordon wall profile (Eq. 38), the correlated opposite winding (Eqs. 36, 46), the variational wall thickness (Eq. 44), and the zero-mode/anomaly-inflow bookkeeping (Section VI C) are all constructed from the stated inputs (quark masses, decay constants, instanton-induced cosine potentials), with no data fitting and no prediction that is simply a renamed fit. The π0 winding case is presented independently of the problematic modulus assumption. The one genuinely load-bearing external premise is the assertion that the pure-QCD η′ condensate phase remains well defined through the 2π wall. Section VIII concedes that the effective theory breaks down there and supplies no QCD computation; the assurance is imported by extrapolation from large-N supersymmetric Yang-Mills wall solutions in the authors' own prior work. That is not a constructional reduction of an equation into its inputs, and the cited SYM result is itself independent, so the circularity is partial and limited; however, the central pure-QCD η′ wall claim does lean on this self-citation. The claimed numerical support (Ref. [22], unpublished and by the same group) is a missing-evidence item rather than a circular step.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

No free parameters are fitted to data: the scales Λ, f_η, m_q, f_φ and the decay constants are inputs from prior literature, and derived quantities (Λ_m, wall thickness L=f/Λ²_m, tensions σ) follow from minimizing the written energy functional. No new entities are introduced; the actors are the known η′, π0, PQ axion, Higgs phases, and condensate phases. The load-bearing premises are the dilute-instanton cosine potential, the large-N supersymmetric Yang-Mills extrapolation for the internal wall structure, the 't Hooft-generated effective Yukawa coupling, the early-strong-QCD scenario of reference [4], and the linear variational ansatz. Premises two and four are the fragile ones: one is an admitted analogy, the other a self-cited scenario asserted to be likely without quantitative argument.

assumptions (7)
  • domain assumption The effective phase potential is the dilute-instanton-gas cosine form, periodic in the anomalous combination θ_φ+θ_η-θ̄, plus a quark-mass cosine term.
    Used throughout Sections V-VI (Eqs. 22, 29, 50). The paper says the exact form is unimportant for topology, but the quantitative wall thickness L=f/Λ²_m and the regime comparison in the Appendix depend on the cosine form.
  • ad hoc to paper The quark condensate magnitude stays non-zero through the η′ wall, so the phase θ_η remains well-defined; this is imported from large-N supersymmetric Yang-Mills domain walls.
    Section VIII: the paper admits the order-parameter EFT breaks down inside the wall and states: 'Extrapolating this result to our case of ordinary QCD with quarks in the fundamental representation, we get the assurance that η′ remains well-defined across the wall.'
  • domain assumption The 't Hooft determinant generates an effective Yukawa coupling Φ ψ̄_L ψ_R (Eq. 47, Figure 2) that sets the light-quark zero-mode chirality on the string.
    Section VI.C; load-bearing for the claim that the minimal string is anomaly-free, since the heavy quark couples to Φ* while the light quark couples to Φ, giving opposite chiralities.
  • domain assumption The early-universe hierarchy can be inverted, f_φ/Λ|_early << 1, because the QCD gauge coupling can be strong during or after inflation.
    Section IX (Eqs. 78-81); the headline cosmological claim depends on the scenario of reference [4], which the paper concedes is 'scenario-dependent' and whose likelihood it asserts without quantitative support.
  • domain assumption The linear variational ansatz (42)-(43) adequately represents the winding profiles, so the conclusion that the L_φ=L_η regime is favored is reliable.
    Appendix (Eqs. 89-95). The exact Sine-Gordon solution (46) for the constrained case partially justifies the ansatz, but the global minimum over all profiles is not proven, and numerical confirmation is deferred to reference [22].
  • standard math Standard QCD vacuum structure: quark masses and the chiral anomaly explicitly break the chiral symmetries, leaving a single minimum (mod 2π) for the condensate phases.
    Sections II-IV; textbook QCD/θ-vacuum background ('t Hooft, Callan-Dashen-Gross, Jackiw-Rebbi), not new content.
  • domain assumption The simplified model with one light and one heavy quark captures the essence of realistic KSVZ and DFSZ axion models.
    Section VII: 'The above-discussed simplified model... captures the essence of the story for fully realistic axion models.' The DFSZ analysis adds further assumptions about Higgs phase couplings (Eqs. 57-65).

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Pith. "Pith review of Cosmic strings and domain walls of the QCD quark condensate with and without a hidden axion." pith.science (2026). https://pith.science/paper/NEKFSL6S

@misc{pith2026250503542,
  author       = {Pith},
  title        = {Pith review of: Cosmic strings and domain walls of the QCD quark condensate with and without a hidden axion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NEKFSL6S}},
  note         = {Machine review of arXiv:2505.03542}
}
abstract

The chiral quark condensate of QCD, which spontaneously breaks the anomalous axial symmetry, gives rise to axionic type global string-wall systems. If a Peccei-Quinn type axion exists in the theory, the axionic strings are in general accompanied by winding of the QCD quark condensate. Depending on the axion model the winding can proceed either in the $\eta'$ or in the pion direction. This determines the structure of fermionic zero modes and the anomaly inflow which has important astrophysical consequences. We point out that $\eta'$ and pion string-wall systems exist in pure QCD, independently of the hidden axion. Strikingly, even if a hidden axion exists, the early cosmology can be entirely dominated by string-wall systems formed by the QCD quark condensate. We also discuss their role in the QCD phase transition and in heavy-ion physics.

Figures

Figures reproduced from arXiv: 2505.03542 by the authors.

Figure 1
Figure 1. FIG. 1: Illustration of the wall profiles for the linear [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: A diagram describing how the effective Yukawa [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Reference graph

Works this paper leans on

87 extracted references · 32 canonical work pages

  1. [22]

    Reduced Limit on the Permanent Electric Dipole Moment of Hg199,

    B. Graner, Y. Chen, E. G. Lindahl, and B. R. Heckel, “Reduced Limit on the Permanent Electric Dipole Moment of Hg199,” Phys. Rev. Lett. 116 no. 16, (2016) 161601, arXiv:1601.04339 [physics.atom-ph] . [Erratum: Phys.Rev.Lett. 119, 119901 (2017)]

    arXiv 2016

  2. [1]

    2)η′ illustrates the reality of axion dynamics: η′ would be an exact quality axion, if at least one quark would be massless [3]

    The mass of η′ represents an experimental proof of the existence of θ-vacua. 2)η′ illustrates the reality of axion dynamics: η′ would be an exact quality axion, if at least one quark would be massless [3]

  3. [2]

    This symmetry is spontaneously broken and, due to the anomaly, it is also explicitly broken

    η′ string-wall system of U(1)A Let’s now turn to the anomalous U(1)A symmetry. This symmetry is spontaneously broken and, due to the anomaly, it is also explicitly broken. Thus, we haveU(1)A strings attached to domain walls. The domain wall appears because of the explicit break- ing, i.e. the cosine potential. Energetically, the phase prefers to stay in t...

  4. [3]

    Since quarks are massive, there must exist a good- quality axion. V. COUPLED SYSTEM In order to understand the mixing between theη′-meson and the PQ axion field, we consider a simplified model that includes a single light quark ψ and a single heavy quark Ψ. The latter gets its mass from the PQ field Φ. In the low energy EFT this model gives rise to an axi...

  5. [4]

    As explained above, this is the U(1) symmetry which is not explicitly but only spontaneously broken

    axion- η′ string of global U(1)V First, we focus on the U(1)V -symmetry. As explained above, this is the U(1) symmetry which is not explicitly but only spontaneously broken. Thus, there exist global strings of U(1)V . Far away from the straight string the two phases wind oppositely: θϕ =−θη =nVφ, (36) where φ is the polar angle in the plane perpendicular ...

  6. [5]

    In the first approximation, the solution is still given by Eq

    η′ string wall system Formψ≪ Λ, the effect of a light quark mass term on the U(1)A string-wall system is insignificant, and it is still dominated by the winding of the θη-phase. In the first approximation, the solution is still given by Eq. (38) with the mass mη slightly shifted by the explicit breaking term as given by Eq. (31)

  7. [6]

    However, the phaseθη continues to fully wind around the string

    η′-axion string wall system The effect of mψ̸= 0 on the would-be U(1)V -string is more dramatic, since a domain wall gets attached to it. However, the phaseθη continues to fully wind around the string. This can be understood in simple terms by analyzing the energy balance among various terms in the energy functional around a large circle of radius R≫m−1 ϕ...

  8. [7]

    Since Λ ≫ Λm, the first cosine in Eq

    The opposite winding in θη =−θϕ, which gets rid of the energy of the Λ 4-term. Since Λ ≫ Λm, the first cosine in Eq. (41) is much more costly in energy

Show all 87 references
  1. [8]

    semi-global

    Limiting the non-trivial winding of the phases to fixed arches, while keeping the rest of the circle in the vacuum. This turns the axionic string into a string-wall system. The winding length can be estimated by balancing the gradient energy and the potential energy. To leadin...

  2. [9]

    Early string cosmology is dominated by PQ strings of the hidden axion

  3. [10]

    Therefore, strings are free of domain walls

    At the moment of string-formation the axion potential vanishes. Therefore, strings are free of domain walls. We argue that the above picture is only valid in a restricted parameter space within a limited class of sce- narios, whereas more generic scenarios are drastically diff...

  4. [11]

    Thus, it is possible that the early epoch hierarchy be- tweenfϕ and Λ is drastically different from its present day value (77)

    appears rather high. Thus, it is possible that the early epoch hierarchy be- tweenfϕ and Λ is drastically different from its present day value (77). In fact, the hierarchy could be as extreme as fϕ Λ early ≪ 1. (81) 13 In this case, not only the potential of θeff is generated ...

  5. [12]

    Superconducting Strings,

    E. Witten, “Superconducting Strings,” Nucl. Phys. B 249 (1985) 557–592

    1985

  6. [13]

    Anomalies and Fermion Zero Modes on Strings and Domain Walls,

    C. G. Callan, Jr. and J. A. Harvey, “Anomalies and Fermion Zero Modes on Strings and Domain Walls,” Nucl. Phys. B 250 (1985) 427–436

    1985

  7. [14]

    Three-form gauging of axion symmetries and gravity,

    G. Dvali, “Three-form gauging of axion symmetries and gravity,” arXiv:hep-th/0507215

    arXiv

  8. [15]

    Removing the cosmological bound on the axion scale,

    G. R. Dvali, “Removing the cosmological bound on the axion scale,” arXiv:hep-ph/9505253

    arXiv

  9. [16]

    The Structure of the Gauge Theory Vacuum,

    C. G. Callan, Jr., R. F. Dashen, and D. J. Gross, “The Structure of the Gauge Theory Vacuum,” Phys. Lett. B 63 (1976) 334–340

    1976

  10. [17]

    Vacuum Periodicity in a Yang-Mills Quantum Theory,

    R. Jackiw and C. Rebbi, “Vacuum Periodicity in a Yang-Mills Quantum Theory,” Phys. Rev. Lett. 37 (1976) 172–175

    1976

  11. [18]

    CP Violating Effects in QCD,

    V. Baluni, “CP Violating Effects in QCD,” Phys. Rev. D 19 (1979) 2227–2230

    1979

  12. [19]

    Chiral Estimate of the Electric Dipole Moment of the Neutron in Quantum Chromodynamics,

    R. J. Crewther, P. Di Vecchia, G. Veneziano, and E. Witten, “Chiral Estimate of the Electric Dipole Moment of the Neutron in Quantum Chromodynamics,” Phys. Lett. B 88 (1979) 123. [Erratum: Phys.Lett.B 91, 487 (1980)]

    1979

  13. [20]

    An Improved experimental limit on the electric dipole moment of the neutron,

    C. A. Baker et al., “An Improved experimental limit on the electric dipole moment of the neutron,” Phys. Rev. Lett. 97 (2006) 131801, arXiv:hep-ex/0602020

    2006 arXiv

  14. [21]

    Revised experimental upper limit on the electric dipole moment of the neutron,

    J. M. Pendlebury et al., “Revised experimental upper limit on the electric dipole moment of the neutron,” Phys. Rev. D 92 no. 9, (2015) 092003, arXiv:1509.04411 [hep-ex]

    2015 arXiv

  15. [23]

    Lefthanded Currents and CP Violation,

    J. R. Ellis, M. K. Gaillard, and D. V. Nanopoulos, “Lefthanded Currents and CP Violation,” Nucl. Phys. B 109 (1976) 213–243

    1976

  16. [24]

    Electric Dipole Moment of Quark in a Gauge Theory with Left-Handed Currents,

    E. P. Shabalin, “Electric Dipole Moment of Quark in a Gauge Theory with Left-Handed Currents,” Sov. J. Nucl. Phys. 28 (1978) 75

    1978

  17. [25]

    Strong and Weak CP Violation,

    J. R. Ellis and M. K. Gaillard, “Strong and Weak CP Violation,” Nucl. Phys. B 150 (1979) 141–162

    1979

  18. [26]

    CP Conservation in the Presence of Instantons,

    R. D. Peccei and H. R. Quinn, “CP Conservation in the Presence of Instantons,” Phys. Rev. Lett. 38 (1977) 1440–1443. R. D. Peccei and H. R. Quinn, “Constraints Imposed by CP Conservation in the Presence of Instantons,” Phys. Rev. D 16 (1977) 1791–1797

    1977

  19. [27]

    A New Light Boson?,

    S. Weinberg, “A New Light Boson?,” Phys. Rev. Lett. 40 (1978) 223–226. F. Wilczek, “Problem of Strong P and T Invariance in the Presence of Instantons,” Phys. Rev. Lett. 40 (1978) 279–282

    1978

  20. [28]

    Parity Conservation in QCD,

    C. Vafa and E. Witten, “Parity Conservation in QCD,” Phys. Rev. Lett. 53 (1984) 535

    1984

  21. [29]

    Symmetry Breaking Through Bell-Jackiw Anomalies,

    G. ’t Hooft, “Symmetry Breaking Through Bell-Jackiw Anomalies,” Phys. Rev. Lett. 37 (1976) 8–11. G. ’t Hooft, “Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle,” Phys. Rev. D 14 (1976) 3432–3450. [Erratum: Phys.Rev.D 18, 2199 (1978)]

    1976

  22. [30]

    Topological mass generation in four dimensions,

    G. Dvali, R. Jackiw, and S.-Y. Pi, “Topological mass generation in four dimensions,” Phys. Rev. Lett. 96 (2006) 081602, arXiv:hep-th/0511175

    2006 arXiv

  23. [31]

    How neutrino protects the axion,

    G. Dvali, S. Folkerts, and A. Franca, “How neutrino protects the axion,” Phys. Rev. D 89 no. 10, (2014) 105025, arXiv:1312.7273 [hep-th]

    2014 arXiv

  24. [32]

    FLAG Review 2024,

    Flavour Lattice Averaging Group (FLAG) Collaboration, Y. Aoki et al., “FLAG Review 2024,” arXiv:2411.04268 [hep-lat]

    2024 arXiv

  25. [33]

    Bachmaier, G

    M. Bachmaier, G. Dvali, L. Komisel, and A. Stuhlfauth in progress

  26. [34]

    Zero Modes of the Vortex - Fermion System,

    R. Jackiw and P. Rossi, “Zero Modes of the Vortex - Fermion System,” Nucl. Phys. B 190 (1981) 681–691

    1981

  27. [35]

    Cosmological Effects of Superconducting Strings,

    J. P. Ostriker, A. C. Thompson, and E. Witten, “Cosmological Effects of Superconducting Strings,” Phys. Lett. B 180 (1986) 231–239

    1986

  28. [36]

    Superconducting Strings in Axion Models,

    G. Lazarides and Q. Shafi, “Superconducting Strings in Axion Models,” Phys. Lett. B 151 (1985) 123–126

    1985

  29. [37]

    Axionic Strings: Covariant Anomalies and Bosonization of Chiral Zero Modes,

    S. G. Naculich, “Axionic Strings: Covariant Anomalies and Bosonization of Chiral Zero Modes,” Nucl. Phys. B 296 (1988) 837–867

    1988

  30. [38]

    The Local structure of anomaly inflow,

    J. A. Harvey and O. Ruchayskiy, “The Local structure of anomaly inflow,” JHEP 06 (2001) 044, arXiv:hep-th/0007037

    2001 arXiv

  31. [39]

    A CMB Millikan 17 experiment with cosmic axiverse strings,

    P. Agrawal, A. Hook, and J. Huang, “A CMB Millikan 17 experiment with cosmic axiverse strings,” JHEP 07 (2020) 138, arXiv:1912.02823 [astro-ph.CO]

    2020 arXiv

  32. [40]

    Axion string signatures: a cosmological plasma collider,

    P. Agrawal, A. Hook, J. Huang, and G. Marques-Tavares, “Axion string signatures: a cosmological plasma collider,” JHEP 01 (2022) 103, arXiv:2010.15848 [hep-ph]

    2022 arXiv

  33. [41]

    Axion strings are superconducting,

    H. Fukuda, A. V. Manohar, H. Murayama, and O. Telem, “Axion strings are superconducting,” JHEP 06 (2021) 052, arXiv:2010.02763 [hep-ph]

    2021 arXiv

  34. [42]

    Zero modes of massive fermions delocalize from axion strings,

    H. Bagherian, K. Fraser, S. Homiller, and J. Stout, “Zero modes of massive fermions delocalize from axion strings,” JHEP 05 (2024) 079, arXiv:2310.01476 [hep-th]

    2024 arXiv

  35. [43]

    Weak Interaction Singlet and Strong CP Invariance,

    J. E. Kim, “Weak Interaction Singlet and Strong CP Invariance,” Phys. Rev. Lett. 43 (1979) 103. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Can Confinement Ensure Natural CP Invariance of Strong Interactions?,” Nucl. Phys. B 166 (1980) 493–506

    1979

  36. [44]

    A Simple Solution to the Strong CP Problem with a Harmless Axion,

    M. Dine, W. Fischler, and M. Srednicki, “A Simple Solution to the Strong CP Problem with a Harmless Axion,” Phys. Lett. B 104 (1981) 199–202. A. R. Zhitnitsky, “On Possible Suppression of the Axion Hadron Interactions. (In Russian),” Sov. J. Nucl. Phys. 31 (1980) 260

    1981

  37. [45]

    Topologically stable electroweak flux tubes,

    G. R. Dvali and G. Senjanovic, “Topologically stable electroweak flux tubes,” Phys. Rev. Lett. 71 (1993) 2376–2379, arXiv:hep-ph/9305278

    1993 arXiv

  38. [46]

    Domain walls in strongly coupled theories,

    G. R. Dvali and M. A. Shifman, “Domain walls in strongly coupled theories,” Phys. Lett. B 396 (1997) 64–69, arXiv:hep-th/9612128. [Erratum: Phys.Lett.B 407, 452 (1997)]

    1997 arXiv

  39. [47]

    Branes and the dynamics of QCD,

    E. Witten, “Branes and the dynamics of QCD,” Nucl. Phys. B 507 (1997) 658–690, arXiv:hep-th/9706109

    1997 arXiv

  40. [48]

    Large N domain walls as D-branes for N=1 QCD string,

    G. R. Dvali and Z. Kakushadze, “Large N domain walls as D-branes for N=1 QCD string,” Nucl. Phys. B 537 (1999) 297–316, arXiv:hep-th/9807140

    1999 arXiv

  41. [49]

    BPS domain walls in large N supersymmetric QCD,

    G. R. Dvali, G. Gabadadze, and Z. Kakushadze, “BPS domain walls in large N supersymmetric QCD,” Nucl. Phys. B 562 (1999) 158–180, arXiv:hep-th/9901032

    1999 arXiv

  42. [50]

    Inflation induced SUSY breaking and flat vacuum directions,

    G. R. Dvali, “Inflation induced SUSY breaking and flat vacuum directions,” Phys. Lett. B 355 (1995) 78–84, arXiv:hep-ph/9503375

    1995 arXiv

  43. [51]

    Brane inflation,

    G. R. Dvali and S. H. H. Tye, “Brane inflation,” Phys. Lett. B 450 (1999) 72–82, arXiv:hep-ph/9812483

    1999 arXiv

  44. [52]

    D-brane inflation,

    G. R. Dvali, Q. Shafi, and S. Solganik, “D-brane inflation,” in 4th European Meeting From the Planck Scale to the Electroweak Scale . 5, 2001. arXiv:hep-th/0105203

    2001 arXiv

  45. [53]

    Cosmology of the Invisible Axion,

    J. Preskill, M. B. Wise, and F. Wilczek, “Cosmology of the Invisible Axion,” Phys. Lett. B 120 (1983) 127–132

    1983

  46. [54]

    The Not So Harmless Axion,

    M. Dine and W. Fischler, “The Not So Harmless Axion,” Phys. Lett. B 120 (1983) 137–141

    1983

  47. [55]

    A Cosmological Bound on the Invisible Axion,

    L. F. Abbott and P. Sikivie, “A Cosmological Bound on the Invisible Axion,” Phys. Lett. B 120 (1983) 133–136

    1983

  48. [56]

    Removing the cosmological bound on the axion scale in the Kim-Shifman-Vainshtein-Zakharov and Dine-Fischler-Srednicki-Zhitnitsky models,

    E. Koutsangelas, “Removing the cosmological bound on the axion scale in the Kim-Shifman-Vainshtein-Zakharov and Dine-Fischler-Srednicki-Zhitnitsky models,” Phys. Rev. D 107 no. 9, (2023) 095009, arXiv:2212.07822 [hep-ph]

    2023 arXiv

  49. [57]

    Semilocal and electroweak strings,

    A. Achucarro and T. Vachaspati, “Semilocal and electroweak strings,” Phys. Rept. 327 (2000) 347–426, arXiv:hep-ph/9904229

    2000 arXiv

  50. [58]

    Cosmic Strings and Domain Walls in Models with Goldstone and PseudoGoldstone Bosons,

    A. Vilenkin and A. E. Everett, “Cosmic Strings and Domain Walls in Models with Goldstone and PseudoGoldstone Bosons,” Phys. Rev. Lett. 48 (1982) 1867–1870

    1982

  51. [59]

    Dynamical Evolution of Domain Walls in an Expanding Universe,

    W. H. Press, B. S. Ryden, and D. N. Spergel, “Dynamical Evolution of Domain Walls in an Expanding Universe,” Astrophys. J. 347 (1989) 590–604

    1989

  52. [60]

    Scaling Properties of Domain Wall Networks,

    A. M. M. Leite and C. J. A. P. Martins, “Scaling Properties of Domain Wall Networks,” Phys. Rev. D 84 (2011) 103523, arXiv:1110.3486 [hep-ph]

    2011 arXiv

  53. [61]

    Summing tree graphs at threshold,

    L. S. Brown, “Summing tree graphs at threshold,” Phys. Rev. D 46 (1992) R4125–R4127, arXiv:hep-ph/9209203

    1992 arXiv

  54. [62]

    Estimate of the onset of nonperturbative particle production at high-energy in a scalar theory,

    M. B. Voloshin, “Estimate of the onset of nonperturbative particle production at high-energy in a scalar theory,” Phys. Lett. B 293 (1992) 389–394

    1992

  55. [63]

    Amplitude estimates for multi - Higgs production at high-energies,

    E. N. Argyres, R. H. P. Kleiss, and C. G. Papadopoulos, “Amplitude estimates for multi - Higgs production at high-energies,” Nucl. Phys. B 391 (1993) 42–56

    1993

  56. [64]

    Nonperturbative production of multiboson states and quantum bubbles,

    A. S. Gorsky and M. B. Voloshin, “Nonperturbative production of multiboson states and quantum bubbles,” Phys. Rev. D 48 (1993) 3843–3851, arXiv:hep-ph/9305219

    1993 arXiv

  57. [65]

    Exponentiation of multiparticle amplitudes in scalar theories,

    M. V. Libanov, V. A. Rubakov, D. T. Son, and S. V. Troitsky, “Exponentiation of multiparticle amplitudes in scalar theories,” Phys. Rev. D 50 (1994) 7553–7569, arXiv:hep-ph/9407381

    1994 arXiv

  58. [66]

    Exponentiation of multiparticle amplitudes in scalar theories. 2. Universality of the exponent,

    M. V. Libanov, D. T. Son, and S. V. Troitsky, “Exponentiation of multiparticle amplitudes in scalar theories. 2. Universality of the exponent,” Phys. Rev. D 52 (1995) 3679–3687, arXiv:hep-ph/9503412

    1995 arXiv

  59. [67]

    Semiclassical approach for multiparticle production in scalar theories,

    D. T. Son, “Semiclassical approach for multiparticle production in scalar theories,” Nucl. Phys. B 477 (1996) 378–406, arXiv:hep-ph/9505338

    1996 arXiv

  60. [68]

    Black hole formation and classicalization in ultra-Planckian 2→N scattering,

    G. Dvali, C. Gomez, R. S. Isermann, D. L¨ ust, and S. Stieberger, “Black hole formation and classicalization in ultra-Planckian 2→N scattering,” Nucl. Phys. B 893 (2015) 187–235, arXiv:1409.7405 [hep-th]

    2015 arXiv

  61. [69]

    Glimpses of black hole formation/evaporation in highly inelastic, ultra-planckian string collisions,

    A. Addazi, M. Bianchi, and G. Veneziano, “Glimpses of black hole formation/evaporation in highly inelastic, ultra-planckian string collisions,” JHEP 02 (2017) 111, arXiv:1611.03643 [hep-th]

    2017 arXiv

  62. [70]

    Classicalization Clearly: Quantum Transition into States of Maximal Memory Storage Capacity,

    G. Dvali, “Classicalization Clearly: Quantum Transition into States of Maximal Memory Storage Capacity,” arXiv:1804.06154 [hep-th]

    arXiv

  63. [71]

    Inconsistencies of higgsplosion,

    A. Monin, “Inconsistencies of higgsplosion,” arXiv:1808.05810 [hep-th]

    arXiv

  64. [72]

    Entropy Bound and Unitarity of Scattering Amplitudes,

    G. Dvali, “Entropy Bound and Unitarity of Scattering Amplitudes,” JHEP 03 (2021) 126, arXiv:2003.05546 [hep-th]

    2021 arXiv

  65. [73]

    Perturbative understanding of nonperturbative processes and quantumization versus classicalization,

    G. Dvali and L. Eisemann, “Perturbative understanding of nonperturbative processes and quantumization versus classicalization,” Phys. Rev. D 106 no. 12, (2022) 125019, arXiv:2211.02618 [hep-th]

    2022 arXiv

  66. [74]

    Classicalization and unitarization of wee partons in QCD and gravity: The CGC-black hole correspondence,

    G. Dvali and R. Venugopalan, “Classicalization and unitarization of wee partons in QCD and gravity: The CGC-black hole correspondence,” Phys. Rev. D 105 no. 5, (2022) 056026, arXiv:2106.11989 [hep-th]

    2022 arXiv

  67. [75]

    The Color Glass Condensate,

    F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan, “The Color Glass Condensate,” Ann. Rev. Nucl. Part. Sci. 60 (2010) 463–489, arXiv:1002.0333 [hep-ph]

    2010 arXiv

  68. [76]

    The ATLAS Experiment at the CERN Large Hadron Collider,

    ATLAS Collaboration, G. Aad et al., “The ATLAS Experiment at the CERN Large Hadron Collider,” JINST 3 (2008) S08003. ALICE Collaboration, K. Aamodt et al., “The ALICE experiment at the CERN LHC,” JINST 3 (2008) S08002

    2008

  69. [77]

    RHIC project 18 overview,

    M. Harrison, T. Ludlam, and S. Ozaki, “RHIC project 18 overview,” Nucl. Instrum. Meth. A 499 (2003) 235–244. S. Ozaki, “The Relativistic heavy ion collider at Brookhaven,” Nucl. Phys. A 525 (1991) 125C–132C

    2003

  70. [78]

    Strong-CP with and without gravity,

    G. Dvali, “Strong-CP with and without gravity,” arXiv:2209.14219 [hep-ph]

    arXiv

  71. [79]

    Consistency of the dual formulation of axion solutions to the strong CP problem,

    O. Sakhelashvili, “Consistency of the dual formulation of axion solutions to the strong CP problem,” Phys. Rev. D 105 no. 8, (2022) 085020, arXiv:2110.03386 [hep-th]

    2022 arXiv

  72. [80]

    Dvali, L

    G. Dvali, L. Komisel, and A. Stuhlfauth in progress

  73. [81]

    Small neutrino masses from gravitationalθ-term,

    G. Dvali and L. Funcke, “Small neutrino masses from gravitationalθ-term,” Phys. Rev. D 93 no. 11, (2016) 113002, arXiv:1602.03191 [hep-ph]

    2016 arXiv

  74. [82]

    Time- and Space-Varying Neutrino Mass Matrix from Soft Topological Defects,

    G. Dvali, L. Funcke, and T. Vachaspati, “Time- and Space-Varying Neutrino Mass Matrix from Soft Topological Defects,” Phys. Rev. Lett. 130 no. 9, (2023) 091601, arXiv:2112.02107 [hep-ph]

    2023 arXiv

  75. [83]

    Hint to supersymmetry from the GR vacuum,

    G. Dvali, A. Kobakhidze, and O. Sakhelashvili, “Hint to supersymmetry from the GR vacuum,” Phys. Rev. D 110 no. 8, (2024) 086008, arXiv:2406.18402 [hep-th]

    2024 arXiv

  76. [84]

    Asymptotically Flat Selfdual Solutions to Euclidean Gravity,

    T. Eguchi and A. J. Hanson, “Asymptotically Flat Selfdual Solutions to Euclidean Gravity,” Phys. Lett. B 74 (1978) 249–251. T. Eguchi and A. J. Hanson, “Selfdual Solutions to Euclidean Gravity,” Annals Phys. 120 (1979) 82

    1978

  77. [85]

    Symmetry Breaking by Instantons in Supergravity,

    S. W. Hawking and C. N. Pope, “Symmetry Breaking by Instantons in Supergravity,” Nucl. Phys. B 146 (1978) 381–392. K. Konishi, N. Magnoli, and H. Panagopoulos, “Spontaneous Breaking of Local Supersymmetry by Gravitational Instantons,” Nucl. Phys. B 309 (1988) 201. K. Konishi, ...

    1978

  78. [86]

    Topologically stable Z strings in the supersymmetric Standard Model,

    G. R. Dvali and G. Senjanovic, “Topologically stable Z strings in the supersymmetric Standard Model,” Phys. Lett. B 331 (1994) 63–68, arXiv:hep-ph/9403277

    1994 arXiv

  79. [87]

    Electroweakηw meson,

    G. Dvali, A. Kobakhidze, and O. Sakhelashvili, “Electroweakηw meson,” arXiv:2408.07535 [hep-th]

    arXiv

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