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arxiv: 2604.17848 · v2 · submitted 2026-04-20 · ✦ hep-lat · hep-th

Recognition: unknown

Adiabatic continuity in a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion

Yudai Hamada , Tatsuhiro Misumi
Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:57 UTC · model grok-4.3

classification ✦ hep-lat hep-th
keywords adiabatic continuitytwisted Eguchi-Kawai modeladjoint Dirac fermionPolyakov loopcenter-symmetric phaselarge-N gauge theoryspatial compactificationvolume independence
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The pith

Numerical evidence from a reduced model indicates the center-symmetric confined phase of large-N gauge theory with one adjoint fermion persists under spatial compactification.

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

The paper tests whether the confined phase in large-N SU(N) gauge theories with adjoint fermions remains stable when one direction is compactified to a small circle. It employs a partially reduced twisted Eguchi-Kawai model on a 1^3 by L4 lattice with an adjoint Wilson fermion to measure the Polyakov loop around the compact direction and order parameters for volume independence. For N=36 and L4=2 in the light-fermion regime with periodic boundary conditions, the Polyakov loop stays near zero as the circle shrinks, while volume-independence parameters remain consistent with zero. These observations support an adiabatic continuity scenario in which the confined phase at large volumes connects smoothly to small volumes. The results hold in the studied parameter range and align with anomaly constraints of the four-dimensional theory, though antiperiodic boundary conditions produce a deconfinement transition.

Core claim

Within the partially reduced TEK model at N=36, L4=2, b from 0.30 to 0.46 and kappa from 0.03 to 0.16, the Polyakov loop around S1 remains near zero in the light-fermion regime under periodic boundary conditions as the circle size decreases, while volume-independence order parameters stay consistent with zero. This supplies numerical evidence, inside the reduced-model setup, for an adiabatic-continuity scenario in which the center-symmetric confined phase is smoothly connected between large and small circles. The scenario is compatible with the anomaly constraints of the underlying four-dimensional theory.

What carries the argument

The partially reduced twisted Eguchi-Kawai model on a 1^3 x L4 lattice with one adjoint Wilson fermion, used to track the Polyakov loop and volume-independence order parameters while reducing computational volume.

If this is right

  • The center-symmetric confined phase remains connected across a range of circle sizes under periodic boundary conditions.
  • Volume independence in the reduced directions holds for the explored parameters and fermion masses.
  • The adiabatic continuity scenario is compatible with the anomaly constraints of the four-dimensional theory.
  • Antiperiodic boundary conditions produce a deconfinement transition instead.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Confirmation at larger N would imply that reduced models can capture four-dimensional large-N confinement physics on small lattices.
  • The same continuity might extend to other representations or numbers of adjoint fermions.
  • The approach offers a route to test whether confinement in higher-dimensional theories survives compactification without phase transitions.

Load-bearing premise

The observations at N=36 and L4=2 in the partially reduced model faithfully represent the phase structure of the full unreduced four-dimensional large-N theory without major finite-N or lattice artifacts.

What would settle it

A statistically clear departure of the Polyakov loop from zero or a violation of volume independence when N is increased or the lattice spacing is decreased would show that the adiabatic continuity does not hold.

Figures

Figures reproduced from arXiv: 2604.17848 by Tatsuhiro Misumi, Yudai Hamada.

Figure 1
Figure 1. Figure 1: FIG. 1. The volume-independence order parameters [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The volume-independence order parameters [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Deconfinement order parameter [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Deconfinement order parameter [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Deconfinement order parameter [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Schematic illustration of confining adiabatic continuity scenario for [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
read the original abstract

We numerically investigate whether the center-symmetric confined phase of large-$N$ $SU(N)$ gauge theory with one adjoint Dirac fermion persists under spatial compactification on $\mathbb{R}^3 \times S^1$. To this end, we employ a partially reduced twisted Eguchi-Kawai (TEK) model on a $1^3 \times L_4$ lattice with an adjoint Wilson fermion, and measure both the Polyakov loop around $S^1$ and order parameters for volume independence in the reduced directions. For $N=36$, $L_4=2$, $b=0.30\text{-}0.46$, and $\kappa=0.03\text{-}0.16$, we find that, with periodic boundary conditions, the Polyakov loop remains near zero in the light-fermion regime as the circle size is reduced. For the modified twist, the volume-independence order parameters are also consistent with zero in the explored region, supporting the validity of the partially reduced description. These results provide numerical evidence, within the reduced-model setup and parameter range studied, for an adiabatic-continuity scenario in which the confined phase is smoothly connected between large and small circles. By contrast, with antiperiodic boundary conditions, the Polyakov loop exhibits a clear deconfinement transition. We also discuss how this scenario is compatible with the anomaly constraints of the underlying four-dimensional theory. The symmetric twist is examined as a useful comparison, although its volume-independence properties appear less robust at the present value of $N$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper numerically investigates the persistence of the center-symmetric confined phase in large-N SU(N) gauge theory with one adjoint Dirac fermion under spatial compactification on R^3 x S^1. Using a partially reduced twisted Eguchi-Kawai model on a 1^3 x L_4 lattice with an adjoint Wilson fermion at N=36 and L_4=2, it measures the Polyakov loop and volume-independence order parameters for b in 0.30-0.46 and kappa in 0.03-0.16. With periodic boundary conditions the Polyakov loop remains near zero in the light-fermion regime, and for the modified twist the volume-independence parameters are consistent with zero; this is presented as evidence for adiabatic continuity between large and small circles. The study contrasts this with a deconfinement transition under antiperiodic boundary conditions and discusses compatibility with 4D anomaly constraints, while noting less robust volume independence for the symmetric twist at this N.

Significance. If the reduced-model results accurately capture the large-N limit without dominant artifacts, the work would supply concrete numerical support for adiabatic-continuity scenarios in adjoint-fermion gauge theories. This strengthens the case that the confined phase can be smoothly connected across compactification radii, with potential implications for lattice studies of large-N confinement and for anomaly-matching arguments in compactified theories. The explicit contrast between periodic and antiperiodic boundary conditions and the use of volume-independence diagnostics are positive features.

major comments (2)
  1. [Numerical results and discussion of volume independence] The central claim that the observations support adiabatic continuity in the full un-reduced 4D large-N theory rests on the assumption that finite-N and reduction artifacts are negligible at N=36, L_4=2. The manuscript notes that the symmetric twist has less robust volume independence at this N, yet provides no quantitative estimate (e.g., comparison runs at larger N or explicit scaling checks) of residual artifacts for the modified twist; this is load-bearing for mapping the reduced-model data to the target theory.
  2. [Results for periodic boundary conditions] No large-N or continuum extrapolation is reported in the explored parameter window (b=0.30-0.46, kappa=0.03-0.16). Because the Polyakov-loop and order-parameter measurements are presented as evidence for the persistence of the confined phase, the absence of such extrapolations leaves open the possibility that the near-zero values are influenced by lattice or finite-N effects rather than reflecting the infinite-N, continuum limit.
minor comments (2)
  1. [Abstract and introduction] The abstract and introduction would benefit from a brief explicit statement of the precise definition of the 'modified twist' versus the symmetric twist, including the twist angles or boundary conditions employed.
  2. [Results section] Figure captions or tables summarizing the Polyakov-loop and order-parameter values should include statistical uncertainties and the number of configurations used, to allow readers to assess the significance of 'near zero' and 'consistent with zero'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the two major comments point by point below, indicating the revisions we intend to make.

read point-by-point responses

  1. Referee: The central claim that the observations support adiabatic continuity in the full un-reduced 4D large-N theory rests on the assumption that finite-N and reduction artifacts are negligible at N=36, L_4=2. The manuscript notes that the symmetric twist has less robust volume independence at this N, yet provides no quantitative estimate (e.g., comparison runs at larger N or explicit scaling checks) of residual artifacts for the modified twist; this is load-bearing for mapping the reduced-model data to the target theory.

    Authors: We agree that controlling finite-N and reduction artifacts is essential for interpreting the reduced-model results in the context of the full 4D large-N theory. The modified twist was deliberately chosen because earlier TEK studies indicate substantially better volume independence at moderate N than the symmetric twist. In our data, the volume-independence order parameters remain consistent with zero within errors for the modified twist across the scanned range, which we view as supporting evidence that residual artifacts are small for the quantities we measure. We will revise the manuscript to expand the discussion of expected 1/N^2 corrections, reference the relevant prior TEK literature, and explicitly state that a dedicated larger-N scaling study lies beyond the present computational resources. This will make the limitations of the current N=36, L_4=2 results clearer while preserving the numerical evidence we report. revision: partial

  2. Referee: No large-N or continuum extrapolation is reported in the explored parameter window (b=0.30-0.46, kappa=0.03-0.16). Because the Polyakov-loop and order-parameter measurements are presented as evidence for the persistence of the confined phase, the absence of such extrapolations leaves open the possibility that the near-zero values are influenced by lattice or finite-N effects rather than reflecting the infinite-N, continuum limit.

    Authors: The b and kappa window was selected to remain inside the scaling region where the gauge coupling is moderate and the fermion mass is light enough to test the adiabatic-continuity hypothesis. The near-zero Polyakov-loop values are stable across several b and kappa points, and this stability is reinforced by the volume-independence diagnostics. We nevertheless accept that explicit extrapolations would strengthen the claim. In the revised manuscript we will add a dedicated paragraph on possible lattice-spacing and finite-N systematics, clarify that our conclusions apply within the reduced-model setup and parameter range explored, and note that a full continuum/large-N extrapolation is left for future work. This will address the referee’s concern without overstating the present results. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results are direct numerical measurements

full rationale

The paper reports lattice simulations of the partially reduced TEK model, measuring Polyakov loop and volume-independence order parameters for specific N=36, L4=2, b and kappa ranges under periodic and antiperiodic boundary conditions. No derivation chain exists that reduces a claimed prediction or first-principles result to fitted inputs or self-citations by construction. The adiabatic-continuity evidence is presented as empirical observation within the reduced-model setup, with no renaming of known results, ansatz smuggling, or uniqueness theorems invoked to force outcomes. Any prior self-citations on TEK reductions are background context, not load-bearing for the central numerical findings, which remain independently falsifiable via the reported observables.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard lattice gauge theory framework, the reduction ansatz of the TEK model, and the choice of parameters to simulate the light fermion regime without additional fitted constants beyond the explored ranges.

free parameters (2)
  • b (inverse coupling)
    Explored in range 0.30-0.46; chosen to probe the relevant regime.
  • kappa (hopping parameter)
    Explored in 0.03-0.16 to access light-fermion regime.
axioms (2)
  • domain assumption The partially reduced twisted Eguchi-Kawai model on a 1^3 x L4 lattice approximates the large-N limit of SU(N) gauge theory with adjoint fermions.
    This is the foundational assumption for the numerical setup.
  • domain assumption The Polyakov loop and volume-independence order parameters correctly identify the confined phase and validity of reduction.
    Standard interpretation in lattice gauge theory.

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discussion (0)

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Reference graph

Works this paper leans on

94 extracted references · 84 canonical work pages · 1 internal anchor

  1. [1]

    A Planar Diagram Theory for Strong Interactions,

    G. ’t Hooft, “A Planar Diagram Theory for Strong Interactions,”Nucl. Phys.B72(1974) 461. 21

    1974

  2. [2]

    Reduction of Dynamical Degrees of Freedom in the Large N Gauge Theory,

    T. Eguchi and H. Kawai, “Reduction of Dynamical Degrees of Freedom in the Large N Gauge Theory,”Phys. Rev. Lett.48(1982) 1063

    1982

  3. [3]

    The Quenched Eguchi-Kawai Model,

    G. Bhanot, U. M. Heller, and H. Neuberger, “The Quenched Eguchi-Kawai Model,”Phys. Lett.113B (1982) 47–50

    1982

  4. [4]

    A Twisted Model for LargeNLattice Gauge Theory,

    A. Gonzalez-Arroyo and M. Okawa, “A Twisted Model for LargeNLattice Gauge Theory,”Phys. Lett. B120(1983) 174–178

    1983

  5. [5]

    The Twisted Eguchi-Kawai Model: A Reduced Model for Large N Lattice Gauge Theory,

    A. Gonzalez-Arroyo and M. Okawa, “The Twisted Eguchi-Kawai Model: A Reduced Model for Large N Lattice Gauge Theory,”Phys. Rev. D27(1983) 2397

    1983

  6. [6]

    Large N reduction in continuum,

    R. Narayanan and H. Neuberger, “Large N reduction in continuum,”Phys. Rev. Lett.91(2003) 081601,arXiv:hep-lat/0303023 [hep-lat]

    work page arXiv 2003

  7. [7]

    Non-perturbative volume-reduction of large-N QCD with adjoint fermions,

    B. Bringoltz and S. R. Sharpe, “Non-perturbative volume-reduction of large-N QCD with adjoint fermions,”Phys. Rev. D80(2009) 065031,arXiv:0906.3538 [hep-lat]

    work page arXiv 2009

  8. [8]

    Large-N reduction in QCD with two adjoint Dirac fermions,

    B. Bringoltz, M. Koren, and S. R. Sharpe, “Large-N reduction in QCD with two adjoint Dirac fermions,”Phys. Rev. D85(2012) 094504,arXiv:1106.5538 [hep-lat]

    work page arXiv 2012

  9. [9]

    The string tension from smeared Wilson loops at large N,

    A. Gonzalez-Arroyo and M. Okawa, “The string tension from smeared Wilson loops at large N,” Phys. Lett. B718(2013) 1524–1528,arXiv:1206.0049 [hep-th]

    work page arXiv 2013

  10. [10]

    Large N meson masses from a matrix model,

    A. Gonz´ alez-Arroyo and M. Okawa, “Large N meson masses from a matrix model,”Phys. Lett. B755 (2016) 132–137,arXiv:1510.05428 [hep-lat]

    work page arXiv 2016

  11. [11]

    Meson spectrum in the largeNlimit,

    M. G. P´ erez, A. Gonz´ alez-Arroyo, and M. Okawa, “Meson spectrum in the largeNlimit,”JHEP04 (2021) 230,arXiv:2011.13061 [hep-lat]

    work page arXiv 2021

  12. [12]

    The large-N limit of the chiral condensate from twisted reduced models,

    C. Bonanno, P. Butti, M. Garc´ ıa Per´ ez, A. Gonz´ alez-Arroyo, K.-I. Ishikawa, and M. Okawa, “The large-N limit of the chiral condensate from twisted reduced models,”JHEP12(2023) 034, arXiv:2309.15540 [hep-lat]

    work page arXiv 2023

  13. [13]

    Gonzalez-Arroyo and M

    A. Gonzalez-Arroyo and M. Okawa, “LargeNreduction with the Twisted Eguchi-Kawai model,” JHEP07(2010) 043,arXiv:1005.1981 [hep-th]

    work page arXiv 2010

  14. [14]

    Perturbative instabilities on the noncommutative torus, Morita duality and twisted boundary conditions,

    Z. Guralnik, R. C. Helling, K. Landsteiner, and E. Lopez, “Perturbative instabilities on the noncommutative torus, Morita duality and twisted boundary conditions,”JHEP05(2002) 025, arXiv:hep-th/0204037

    work page arXiv 2002

  15. [15]

    A Non-perturbative study of 4-D U(1) non-commutative gauge theory: The Fate of one-loop instability,

    W. Bietenholz, J. Nishimura, Y. Susaki, and J. Volkholz, “A Non-perturbative study of 4-D U(1) non-commutative gauge theory: The Fate of one-loop instability,”JHEP10(2006) 042, arXiv:hep-th/0608072

    work page arXiv 2006

  16. [16]

    Symmetry breaking in twisted Eguchi–Kawai models,

    M. Teper and H. Vairinhos, “Symmetry breaking in twisted Eguchi–Kawai models,”Phys. Lett. B 652(2007) 359–369,arXiv:hep-th/0612097

    work page arXiv 2007

  17. [17]

    Large-N reduction in QCD-like theories with massive adjoint fermions,

    T. Azeyanagi, M. Hanada, M. Unsal, and R. Yacoby, “Large-N reduction in QCD-like theories with massive adjoint fermions,”Phys. Rev. D82(2010) 125013,arXiv:1006.0717 [hep-th]

    work page arXiv 2010

  18. [18]

    Twisted reduction in large N QCD with two adjoint Wilson fermions,

    A. Gonzalez-Arroyo and M. Okawa, “Twisted reduction in large N QCD with two adjoint Wilson fermions,”PoSLATTICE2012(2012) 046,arXiv:1210.7881 [hep-lat]. 22

    work page arXiv 2012

  19. [19]

    Twisted space-time reduced model of large N QCD with two adjoint Wilson fermions,

    A. Gonz´ alez-Arroyo and M. Okawa, “Twisted space-time reduced model of large N QCD with two adjoint Wilson fermions,”Phys. Rev. D88(2013) 014514,arXiv:1305.6253 [hep-lat]

    work page arXiv 2013

  20. [20]

    Twisted reduction in largeNQCD with adjoint Wilson fermions,

    A. Gonz´ alez-Arroyo and M. Okawa, “Twisted reduction in largeNQCD with adjoint Wilson fermions,” inKMI-GCOE Workshop on Strong Coupling Gauge Theories in the LHC Perspective, pp. 352–358. 2014.arXiv:1304.0306 [hep-lat]

    work page arXiv 2014

  21. [21]

    Mass anomalous dimension from large N twisted volume reduction,

    M. Garcia Perez, A. Gonzalez-Arroyo, L. Keegan, and M. Okawa, “Mass anomalous dimension from large N twisted volume reduction,”PoSLATTICE2013(2014) 098,arXiv:1311.2395 [hep-lat]

    work page arXiv 2014

  22. [22]

    Mass anomalous dimension of Adjoint QCD at large N from twisted volume reduction,

    M. Garc´ ıa P´ erez, A. Gonz´ alez-Arroyo, L. Keegan, and M. Okawa, “Mass anomalous dimension of Adjoint QCD at large N from twisted volume reduction,”JHEP08(2015) 034,arXiv:1506.06536 [hep-lat]

    work page arXiv 2015

  23. [23]

    ZN stability and continuity in the twisted Eguchi-Kawai model with two-flavor adjoint fermions,

    Y. Hamada and T. Misumi, “ZN stability and continuity in the twisted Eguchi-Kawai model with two-flavor adjoint fermions,”Phys. Rev. D112no. 9, (2025) 094503,arXiv:2507.20123 [hep-lat]

    work page arXiv 2025

  24. [24]

    A FINITE TEMPERATURE TWISTED EGUCHI-KAWAI MODEL,

    A. Gocksch, P. Rossi, and F. Neri, “A FINITE TEMPERATURE TWISTED EGUCHI-KAWAI MODEL,”Phys. Lett. B130(1983) 407–410

    1983

  25. [25]

    The Deconfining Phase Transition in the Finite Temperature Twisted Eguchi-kawai Model,

    A. Gocksch, F. Neri, and P. Rossi, “The Deconfining Phase Transition in the Finite Temperature Twisted Eguchi-kawai Model,”Nucl. Phys. B238(1984) 674–682

    1984

  26. [26]

    Gluino condensate and magnetic monopoles in supersymmetric gluodynamics

    N. M. Davies, T. J. Hollowood, V. V. Khoze, and M. P. Mattis, “Gluino condensate and magnetic monopoles in supersymmetric gluodynamics,”Nucl. Phys. B559(1999) 123–142, arXiv:hep-th/9905015

    work page arXiv 1999

  27. [27]

    Monopoles, affine algebras and the gluino condensate,

    N. M. Davies, T. J. Hollowood, and V. V. Khoze, “Monopoles, affine algebras and the gluino condensate,”J. Math. Phys.44(2003) 3640–3656,arXiv:hep-th/0006011 [hep-th]

    work page arXiv 2003

  28. [28]

    Unsal,Abelian duality, confinement, and chiral symmetry breaking in QCD(adj),Phys

    M. Unsal, “Abelian duality, confinement, and chiral symmetry breaking in QCD(adj),”Phys. Rev. Lett.100(2008) 032005,arXiv:0708.1772 [hep-th]

    work page arXiv 2008

  29. [29]

    Unsal,Magnetic bion condensation: A New mechanism of confinement and mass gap in four dimensions, Phys

    M. Unsal, “Magnetic bion condensation: A New mechanism of confinement and mass gap in four dimensions,”Phys. Rev.D80(2009) 065001,arXiv:0709.3269 [hep-th]

    work page arXiv 2009

  30. [30]

    Volume independence in large N(c) QCD-like gauge theories,

    P. Kovtun, M. Unsal, and L. G. Yaffe, “Volume independence in large N(c) QCD-like gauge theories,” JHEP06(2007) 019,arXiv:hep-th/0702021 [HEP-TH]

    work page arXiv 2007

  31. [31]

    QCD-like Theories on R(3) x S(1): A Smooth Journey from Small to Large r(S(1)) with Double-Trace Deformations,

    M. Shifman and M. Unsal, “QCD-like Theories on R(3) x S(1): A Smooth Journey from Small to Large r(S(1)) with Double-Trace Deformations,”Phys. Rev.D78(2008) 065004,arXiv:0802.1232 [hep-th]

    work page arXiv 2008

  32. [32]

    Large-N volume independence in conformal and confining gauge theories,

    M. Unsal and L. G. Yaffe, “Large-N volume independence in conformal and confining gauge theories,” JHEP08(2010) 030,arXiv:1006.2101 [hep-th]

    work page arXiv 2010

  33. [33]

    Conformality or confinement: (IR)relevance of topological excitations,

    E. Poppitz and M. Unsal, “Conformality or confinement: (IR)relevance of topological excitations,” JHEP09(2009) 050,arXiv:0906.5156 [hep-th]

    work page arXiv 2009

  34. [34]

    Microscopic Structure of Magnetic Bions,

    M. M. Anber and E. Poppitz, “Microscopic Structure of Magnetic Bions,”JHEP06(2011) 136, arXiv:1105.0940 [hep-th]

    work page arXiv 2011

  35. [35]

    Continuity, Deconfinement, and (Super) Yang-Mills Theory,

    E. Poppitz, T. Sch¨ afer, and M. ¨Unsal, “Continuity, Deconfinement, and (Super) Yang-Mills Theory,” 23 JHEP10(2012) 115,arXiv:1205.0290 [hep-th]

    work page arXiv 2012

  36. [36]

    Misumi and T

    T. Misumi and T. Kanazawa, “Adjoint QCD onR 3 ×S 1 with twisted fermionic boundary conditions,”JHEP06(2014) 181,arXiv:1405.3113 [hep-ph]

    work page arXiv 2014

  37. [37]

    From 4d Yang-Mills to 2dCP N−1 model: IR problem and confinement at weak coupling,

    M. Yamazaki and K. Yonekura, “From 4d Yang-Mills to 2dCP N−1 model: IR problem and confinement at weak coupling,”JHEP07(2017) 088,arXiv:1704.05852 [hep-th]

    work page arXiv 2017

  38. [38]

    Anomaly constraints on deconfinement and chiral phase transition

    H. Shimizu and K. Yonekura, “Anomaly constraints on deconfinement and chiral phase transition,” Phys. Rev.D97no. 10, (2018) 105011,arXiv:1706.06104 [hep-th]

    work page arXiv 2018

  39. [39]

    Circle compactification and ’t Hooft anomaly,

    Y. Tanizaki, T. Misumi, and N. Sakai, “Circle compactification and ’t Hooft anomaly,”JHEP12 (2017) 056,arXiv:1710.08923 [hep-th]

    work page arXiv 2017

  40. [40]

    Anomaly matching for the phase diagram of masslessZ N-QCD

    Y. Tanizaki, Y. Kikuchi, T. Misumi, and N. Sakai, “Anomaly matching for phase diagram of massless ZN-QCD,”Phys. Rev.D97(2018) 054012,arXiv:1711.10487 [hep-th]

    work page arXiv 2018

  41. [41]

    Hongo, T

    M. Hongo, T. Misumi, and Y. Tanizaki, “Phase structure of the twistedSU(3)/U(1) 2 flag sigma model onR×S 1,”JHEP02(2019) 070,arXiv:1812.02259 [hep-th]

    work page arXiv 2019

  42. [42]

    Fractionalθangle, ’t Hooft anomaly, and quantum instantons in charge-qmulti-flavor Schwinger model,

    T. Misumi, Y. Tanizaki, and M. ¨Unsal, “Fractionalθangle, ’t Hooft anomaly, and quantum instantons in charge-qmulti-flavor Schwinger model,”JHEP07(2019) 018,arXiv:1905.05781 [hep-th]

    work page arXiv 2019

  43. [43]

    Fujimori, E

    T. Fujimori, E. Itou, T. Misumi, M. Nitta, and N. Sakai, “Confinement-deconfinement crossover in the latticeCP N−1 model,”Phys. Rev. D100no. 9, (2019) 094506,arXiv:1907.06925 [hep-th]

    work page arXiv 2019

  44. [44]

    Misumi, T

    T. Misumi, T. Fujimori, E. Itou, M. Nitta, and N. Sakai, “Lattice study on the twistedCP N−1 models onR×S 1,”PoSLATTICE2019(2019) 015,arXiv:1911.07398 [hep-lat]

    work page arXiv 2019

  45. [45]

    Fujimori, E

    T. Fujimori, E. Itou, T. Misumi, M. Nitta, and N. Sakai, “LatticeCP N−1 model withZ N twisted boundary condition: bions, adiabatic continuity and pseudo-entropy,”JHEP08no. 08, (2020) 011, arXiv:2006.05106 [hep-th]

    work page arXiv 2020

  46. [46]

    Ünsal,Strongly coupled QFT dynamics via TQFT coupling,JHEP11(2021) 134, [2007.03880]

    M. ¨Unsal, “Strongly coupled QFT dynamics via TQFT coupling,”JHEP11(2021) 134, arXiv:2007.03880 [hep-th]

    work page arXiv 2021

  47. [47]

    Poppitz,Notes on Confinement on R3×S1: From Yang–Mills, Super-Yang–Mills, and QCD (adj) to QCD(F),Symmetry14(2022) 180 [2111.10423]

    E. Poppitz, “Notes on Confinement on R3×S1: From Yang–Mills, Super-Yang–Mills, and QCD (adj) to QCD(F),”Symmetry14no. 1, (2022) 180,arXiv:2111.10423 [hep-th]

    work page arXiv 2022

  48. [48]

    Tanizaki and M

    Y. Tanizaki and M. ¨Unsal, “Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications,”PTEP2022(2022) 04A108,arXiv:2201.06166 [hep-th]

    work page arXiv 2022

  49. [49]

    Semiclassics with ’t Hooft flux background for QCD with 2-index quarks,

    Y. Tanizaki and M. ¨Unsal, “Semiclassics with ’t Hooft flux background for QCD with 2-index quarks,”JHEP08(2022) 038,arXiv:2205.11339 [hep-th]

    work page arXiv 2022

  50. [50]

    Semiclassical analysis of the bifundamental QCD onR 2 ×T 2 with ’t Hooft flux,

    Y. Hayashi, Y. Tanizaki, and H. Watanabe, “Semiclassical analysis of the bifundamental QCD onR 2 ×T 2 with ’t Hooft flux,”JHEP10(2023) 146,arXiv:2307.13954 [hep-th]

    work page arXiv 2023

  51. [51]

    Semiclassics for the QCD vacuum structure through T2-compactification with the baryon-’t Hooft flux,

    Y. Hayashi and Y. Tanizaki, “Semiclassics for the QCD vacuum structure through T2-compactification with the baryon-’t Hooft flux,”JHEP08(2024) 001,arXiv:2402.04320 [hep-th]

    work page arXiv 2024

  52. [52]

    Non-supersymmetric duality cascade of QCD(BF) via semiclassics onR 2×T 2 with the baryon-’t Hooft flux,

    Y. Hayashi, Y. Tanizaki, and H. Watanabe, “Non-supersymmetric duality cascade of QCD(BF) via semiclassics onR 2×T 2 with the baryon-’t Hooft flux,”JHEP07(2024) 033,arXiv:2404.16803 24 [hep-th]

    work page arXiv 2024

  53. [53]

    Hayashi and Y

    Y. Hayashi and Y. Tanizaki, “Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism,”Phys. Rev. Lett.133no. 17, (2024) 171902,arXiv:2405.12402 [hep-th]

    work page arXiv 2024

  54. [54]

    Monopole-vortex continuity ofN= 1 super Yang-Mills theory onR 2 ×S 1 ×S 1 with ’t Hooft twist,

    Y. Hayashi, T. Misumi, and Y. Tanizaki, “Monopole-vortex continuity ofN= 1 super Yang-Mills theory onR 2 ×S 1 ×S 1 with ’t Hooft twist,”arXiv:2410.21392 [hep-th]

    work page arXiv

  55. [55]

    Güvendik, T

    C. G¨ uvendik, T. Schaefer, and M. ¨Unsal, “The metamorphosis of semi-classical mechanisms of confinement: From monopoles onR 3 ×S 1 to center-vortices onR 2 ×T 2,”arXiv:2405.13696 [hep-th]

    work page arXiv

  56. [56]

    Higher-order gaugino condensates on a twistedT 4: In the beginning, there was semi-classics,

    M. M. Anber and E. Poppitz, “Higher-order gaugino condensates on a twistedT 4: In the beginning, there was semi-classics,”arXiv:2408.16058 [hep-th]

    work page arXiv

  57. [57]

    Fractional instantons in 2dCP N−1 model and 4d Yang-Mills theory with ’t Hooft twists,

    Y. Hayashi, T. Misumi, M. Nitta, K. Ohashi, and Y. Tanizaki, “Fractional instantons in 2dCP N−1 model and 4d Yang-Mills theory with ’t Hooft twists,”arXiv:2507.12802 [hep-th]

    work page arXiv

  58. [58]

    On 2d perimeter law inN= 1 super Yang-Mills theory on R2 ×S 1 ×S 1 with ’t Hooft twist from Monopole-Vortex continuity,

    Y. Hayashi, T. Misumi, and Y. Tanizaki, “On 2d perimeter law inN= 1 super Yang-Mills theory on R2 ×S 1 ×S 1 with ’t Hooft twist from Monopole-Vortex continuity,”Int. J. Mod. Phys. A41no. 07, (2026) 2548006

    2026

  59. [59]

    Tachyonic instabilities in 2 + 1 dimensional Yang–Mills theory and its connection to number theory,

    F. Chamizo and A. Gonzalez-Arroyo, “Tachyonic instabilities in 2 + 1 dimensional Yang–Mills theory and its connection to number theory,”J. Phys. A50no. 26, (2017) 265401,arXiv:1610.07972 [hep-th]

    work page arXiv 2017

  60. [60]

    Center-vortex semiclassics with non-minimal ’t Hooft fluxes onR 2 ×T 2 and center stabilization at largeN,

    Y. Hayashi, Y. Tanizaki, and M. ¨Unsal, “Center-vortex semiclassics with non-minimal ’t Hooft fluxes onR 2 ×T 2 and center stabilization at largeN,”arXiv:2505.07467 [hep-th]

    work page arXiv

  61. [61]

    The conformal window on the lattice,

    L. Del Debbio, “The conformal window on the lattice,”PoSLattice2010(2014) 004, arXiv:1102.4066 [hep-lat]

    work page arXiv 2014

  62. [62]

    SU(2) gauge theory with one and two adjoint fermions towards the continuum limit

    A. Athenodorou, E. Bennett, G. Bergner, P. Butti, J. Lenz, and B. Lucini, “SU(2) gauge theory with one and two adjoint fermions toward the continuum limit,”Phys. Rev. D113no. 7, (2026) 074505, arXiv:2408.00171 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  63. [63]

    Gonz´ alez-Arroyo and M

    A. Gonz´ alez-Arroyo and M. Okawa, in private communication(2025)

    2025

  64. [64]

    Theta, Time Reversal, and Temperature

    D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, “Theta, Time Reversal, and Temperature,”JHEP05(2017) 091,arXiv:1703.00501 [hep-th]

    work page Pith review arXiv 2017

  65. [65]

    Anomaly matching in QCD thermal phase transition,

    K. Yonekura, “Anomaly matching in QCD thermal phase transition,”JHEP05(2019) 062, arXiv:1901.08188 [hep-th]

    work page arXiv 2019

  66. [66]

    The mixed 0-form/1-form anomaly in Hilbert space: pouring the new wine into old bottles,

    A. A. Cox, E. Poppitz, and F. D. Wandler, “The mixed 0-form/1-form anomaly in Hilbert space: pouring the new wine into old bottles,”JHEP10(2021) 069,arXiv:2106.11442 [hep-th]

    work page arXiv 2021

  67. [67]

    Order parameters and color-flavor center symmetry in QCD,

    A. Cherman, S. Sen, M. Unsal, M. L. Wagman, and L. G. Yaffe, “Order parameters and color-flavor center symmetry in QCD,”Phys. Rev. Lett.119no. 22, (2017) 222001,arXiv:1706.05385 [hep-th]

    work page arXiv 2017

  68. [68]

    Quark-gluon thermodynamics with the Z(N(c)) symmetry,

    H. Kouno, Y. Sakai, T. Makiyama, K. Tokunaga, T. Sasaki, and M. Yahiro, “Quark-gluon thermodynamics with the Z(N(c)) symmetry,”J. Phys.G39(2012) 085010

    2012

  69. [69]

    The quarkyonic phase and the Z Nc symmetry,

    Y. Sakai, H. Kouno, T. Sasaki, and M. Yahiro, “The quarkyonic phase and the Z Nc symmetry,”Phys. 25 Lett.B718(2012) 130–135,arXiv:1204.0228 [hep-ph]

    work page arXiv 2012

  70. [70]

    Confinement andZ 3 symmetry in three-flavor QCD,

    H. Kouno, T. Makiyama, T. Sasaki, Y. Sakai, and M. Yahiro, “Confinement andZ 3 symmetry in three-flavor QCD,”J. Phys.G40(2013) 095003,arXiv:1301.4013 [hep-ph]

    work page arXiv 2013

  71. [71]

    Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories,

    H. Kouno, T. Misumi, K. Kashiwa, T. Makiyama, T. Sasaki, and M. Yahiro, “Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories,”Phys. Rev.D88 no. 1, (2013) 016002,arXiv:1304.3274 [hep-ph]

    work page arXiv 2013

  72. [72]

    Understanding QCD at high density from a Z 3-symmetric QCD-like theory,

    H. Kouno, K. Kashiwa, J. Takahashi, T. Misumi, and M. Yahiro, “Understanding QCD at high density from a Z 3-symmetric QCD-like theory,”Phys. Rev.D93no. 5, (2016) 056009, arXiv:1504.07585 [hep-ph]

    work page arXiv 2016

  73. [73]

    Lattice study on QCD-like theory with exact center symmetry,

    T. Iritani, E. Itou, and T. Misumi, “Lattice study on QCD-like theory with exact center symmetry,” JHEP11(2015) 159,arXiv:1508.07132 [hep-lat]

    work page arXiv 2015

  74. [74]

    Finite-temperature phase transition ofN f = 3 QCD with exact center symmetry,

    T. Misumi, T. Iritani, and E. Itou, “Finite-temperature phase transition ofN f = 3 QCD with exact center symmetry,”PoSLATTICE2015(2016) 152,arXiv:1510.07227 [hep-lat]

    work page arXiv 2016

  75. [75]

    Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching,

    G. V. Dunne, Y. Tanizaki, and M. ¨Unsal, “Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching,”JHEP08(2018) 068,arXiv:1803.02430 [hep-th]

    work page arXiv 2018

  76. [76]

    The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects,

    P. C. Argyres and M. Unsal, “The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects,”JHEP08(2012) 063,arXiv:1206.1890 [hep-th]

    work page arXiv 2012

  77. [77]

    A semiclassical realization of infrared renormalons,

    P. Argyres and M. Unsal, “A semiclassical realization of infrared renormalons,”Phys. Rev. Lett.109 (2012) 121601,arXiv:1204.1661 [hep-th]

    work page arXiv 2012

  78. [78]

    Dunne and M

    G. V. Dunne and M. Unsal, “Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model,”JHEP11(2012) 170,arXiv:1210.2423 [hep-th]

    work page arXiv 2012

  79. [79]

    Continuity and Resurgence: towards a continuum definition of the CP(N-1) model,

    G. V. Dunne and M. Unsal, “Continuity and Resurgence: towards a continuum definition of the CP(N-1) model,”Phys. Rev.D87(2013) 025015,arXiv:1210.3646 [hep-th]

    work page arXiv 2013

  80. [80]

    Misumi, M

    T. Misumi, M. Nitta, and N. Sakai, “Neutral bions in theCP N−1 model,”JHEP06(2014) 164, arXiv:1404.7225 [hep-th]

    work page arXiv 2014

Showing first 80 references.