Abstract
We study an ’t Hooft anomaly of massless QCD at finite temperature. With the imaginary baryon chemical potential at the Roberge-Weiss point, there is a ℤ2 symmetry which can be used to define confinement. We show the existence of a mixed anomaly between the ℤ2 symmetry and the chiral symmetry, which gives a strong relation between confinement and chiral symmetry breaking. The anomaly is a parity anomaly in the QCD Lagrangian reduced to three dimensions. It is reproduced in the chiral Lagrangian by a topological term related to Skyrmion charge, matching the anomaly before and after QCD phase transition. The effect of the imaginary chemical potential is suppresssed in the large N expansion, and we discuss implications of the ’t Hooft anomaly matching for the nature of QCD phase transition with and without the imaginary chemical potential. Arguments based on universality alone are disfavored, and a first order phase transition may be the simplest possibility if the large N expansion is qualitatively good.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y. Aoki, G. Endrodi, Z. Fodor, S.D. Katz and K.K. Szabo, The Order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature 443 (2006) 675 [hep-lat/0611014] [INSPIRE].
T. Bhattacharya et al., QCD Phase Transition with Chiral Quarks and Physical Quark Masses, Phys. Rev. Lett. 113 (2014) 082001 [arXiv:1402.5175] [INSPIRE].
R.D. Pisarski and F. Wilczek, Remarks on the Chiral Phase Transition in Chromodynamics, Phys. Rev. D 29 (1984) 338 [INSPIRE].
S. Aoki, H. Fukaya and Y. Taniguchi, Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature, Phys. Rev. D 86 (2012) 114512 [arXiv:1209.2061] [INSPIRE].
JLQCD collaboration, Can axial U(1) anomaly disappear at high temperature?, EPJ Web Conf. 175 (2018) 01012 [arXiv:1712.05536] [INSPIRE].
TWQCD collaboration, Chiral symmetry and axial U(1) symmetry in finite temperature QCD with domain-wall fermion, PoS(LATTICE2013)165 (2014) [arXiv:1311.6220] [INSPIRE].
Y. Nakayama and T. Ohtsuki, Bootstrapping phase transitions in QCD and frustrated spin systems, Phys. Rev. D 91 (2015) 021901 [arXiv:1407.6195] [INSPIRE].
K. Fukushima and T. Hatsuda, The phase diagram of dense QCD, Rept. Prog. Phys. 74 (2011) 014001 [arXiv:1005.4814] [INSPIRE].
H.-T. Ding, Lattice QCD at nonzero temperature and density, PoS(LATTICE2016)022 (2017) [arXiv:1702.00151] [INSPIRE].
Y. Aoki, Finite temperature QCD: phase transition, topology, and axion, available, in the mixture of Japanese and English, at http://www2.yukawa.kyoto-u.ac.jp/~ppp.ws/PPP2018/slides/aoki.pdf.
D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, Theta, Time Reversal and Temperature, JHEP 05 (2017) 091 [arXiv:1703.00501] [INSPIRE].
H. Itoyama and A.H. Mueller, The Axial Anomaly at Finite Temperature, Nucl. Phys. B 218 (1983) 349 [INSPIRE].
S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Cambridge University Press (2013) [INSPIRE].
Y. Tachikawa and K. Yonekura, Gauge interactions and topological phases of matter, PTEP 2016 (2016) 093B07 [arXiv:1604.06184] [INSPIRE].
M. Yamazaki and K. Yonekura, From 4d Yang-Mills to 2d ℂℙN − 1 model: IR problem and confinement at weak coupling, JHEP 07 (2017) 088 [arXiv:1704.05852] [INSPIRE].
Y. Tanizaki and Y. Kikuchi, Vacuum structure of bifundamental gauge theories at finite topological angles, JHEP 06 (2017) 102 [arXiv:1705.01949] [INSPIRE].
Z. Komargodski, T. Sulejmanpasic and M. Ünsal, Walls, anomalies and deconfinement in quantum antiferromagnets, Phys. Rev. B 97 (2018) 054418 [arXiv:1706.05731] [INSPIRE].
H. Shimizu and K. Yonekura, Anomaly constraints on deconfinement and chiral phase transition, Phys. Rev. D 97 (2018) 105011 [arXiv:1706.06104] [INSPIRE].
Y. Kikuchi and Y. Tanizaki, Global inconsistency, ’t Hooft anomaly and level crossing in quantum mechanics, PTEP 2017 (2017) 113B05 [arXiv:1708.01962] [INSPIRE].
D. Gaiotto, Z. Komargodski and N. Seiberg, Time-reversal breaking in QCD 4 , walls and dualities in 2 + 1 dimensions, JHEP 01 (2018) 110 [arXiv:1708.06806] [INSPIRE].
E. Poppitz and M.E. Shalchian T., String tensions in deformed Yang-Mills theory, JHEP 01 (2018) 029 [arXiv:1708.08821] [INSPIRE].
P. Di Vecchia, G. Rossi, G. Veneziano and S. Yankielowicz, Spontaneous CP breaking in QCD and the axion potential: an effective Lagrangian approach, JHEP 12 (2017) 104 [arXiv:1709.00731] [INSPIRE].
R. Kitano, T. Suyama and N. Yamada, θ = π in SU(N)/ℤN gauge theories, JHEP 09 (2017) 137 [arXiv:1709.04225] [INSPIRE].
Y. Tanizaki, T. Misumi and N. Sakai, Circle compactification and ’t Hooft anomaly, JHEP 12 (2017) 056 [arXiv:1710.08923] [INSPIRE].
M. Yamazaki, Relating ’t Hooft Anomalies of 4d Pure Yang-Mills and 2d ℂℙN − 1 Model, JHEP 10 (2018) 172 [arXiv:1711.04360] [INSPIRE].
Y. Tanizaki, Y. Kikuchi, T. Misumi and N. Sakai, Anomaly matching for the phase diagram of massless ℤN -QCD, Phys. Rev. D 97 (2018) 054012 [arXiv:1711.10487] [INSPIRE].
A. Cherman and M. Ünsal, Critical behavior of gauge theories and Coulomb gases in three and four dimensions, arXiv:1711.10567 [INSPIRE].
M. Guo, P. Putrov and J. Wang, Time reversal, SU(N ) Yang-Mills and cobordisms: Interacting topological superconductors/insulators and quantum spin liquids in 3+1D, Annals Phys. 394 (2018) 244 [arXiv:1711.11587] [INSPIRE].
P. Draper, Domain Walls and the CP Anomaly in Softly Broken Supersymmetric QCD, Phys. Rev. D 97 (2018) 085003 [arXiv:1801.05477] [INSPIRE].
N. Seiberg, Y. Tachikawa and K. Yonekura, Anomalies of Duality Groups and Extended Conformal Manifolds, PTEP 2018 (2018) 073B04 [arXiv:1803.07366] [INSPIRE].
M. Shifman, Supersymmetric tools in Yang-Mills theories at strong coupling: The beginning of a long journey, Int. J. Mod. Phys. A 33 (2018) 1830009 [arXiv:1804.01191] [INSPIRE].
A. Ritz and A. Shukla, Domain wall moduli in softly-broken SQCD at \( \overline{\theta}=\pi \), Phys. Rev. D 97 (2018) 105015 [arXiv:1804.01978] [INSPIRE].
K. Aitken, A. Cherman and M. Ünsal, Dihedral symmetry in SU(N) Yang-Mills theory, arXiv:1804.05845 [INSPIRE].
K. Aitken, A. Cherman and M. Ünsal, Vacuum structure of Yang-Mills theory as a function of θ, JHEP 09 (2018) 030 [arXiv:1804.06848] [INSPIRE].
M.M. Anber and E. Poppitz, Two-flavor adjoint QCD, Phys. Rev. D 98 (2018) 034026 [arXiv:1805.12290] [INSPIRE].
R. Argurio, M. Bertolini, F. Bigazzi, A.L. Cotrone and P. Niro, QCD domain walls, Chern-Simons theories and holography, JHEP 09 (2018) 090 [arXiv:1806.08292] [INSPIRE].
C. Córdova and T.T. Dumitrescu, Candidate Phases for SU(2) Adjoint QCD 4 with Two Flavors from \( \mathcal{N}=2 \) Supersymmetric Yang-Mills Theory, arXiv:1806.09592 [INSPIRE].
M.M. Anber and E. Poppitz, Anomaly matching, (axial) Schwinger models and high-T super Yang-Mills domain walls, JHEP 09 (2018) 076 [arXiv:1807.00093] [INSPIRE].
Y. Tanizaki, Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking, JHEP 08 (2018) 171 [arXiv:1807.07666] [INSPIRE].
Z. Bi and T. Senthil, An Adventure in Topological Phase Transitions in 3+1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality, arXiv:1808.07465 [INSPIRE].
S. Yamaguchi, ’t Hooft anomaly matching condition and chiral symmetry breaking without bilinear condensate, JHEP 01 (2019) 014 [arXiv:1811.09390] [INSPIRE].
M.M. Anber and E. Poppitz, Domain walls in high-T SU(N ) super Yang-Mills theory and QCD(adj), arXiv:1811.10642 [INSPIRE].
V. Bashmakov, F. Benini, S. Benvenuti and M. Bertolini, Living on the walls of super-QCD, SciPost Phys. 6 (2019) 044 [arXiv:1812.04645] [INSPIRE].
P.-S. Hsin, H.T. Lam and N. Seiberg, Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d, SciPost Phys. 6 (2019) 039 [arXiv:1812.04716] [INSPIRE].
Z. Wan and J. Wang, New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and ℂℙN − 1 σ-model, arXiv:1812.11968 [INSPIRE].
M.G. Alford, A. Kapustin and F. Wilczek, Imaginary chemical potential and finite fermion density on the lattice, Phys. Rev. D 59 (1999) 054502 [hep-lat/9807039] [INSPIRE].
M.-P. Lombardo, Finite density (might well be easier) at finite temperature, Nucl. Phys. Proc. Suppl. 83 (2000) 375 [hep-lat/9908006] [INSPIRE].
P. de Forcrand and O. Philipsen, The QCD phase diagram for small densities from imaginary chemical potential, Nucl. Phys. B 642 (2002) 290 [hep-lat/0205016] [INSPIRE].
P. de Forcrand and O. Philipsen, The QCD phase diagram for three degenerate flavors and small baryon density, Nucl. Phys. B 673 (2003) 170 [hep-lat/0307020] [INSPIRE].
P. de Forcrand and O. Philipsen, The Chiral critical line of N f = 2 + 1 QCD at zero and non-zero baryon density, JHEP 01 (2007) 077 [hep-lat/0607017] [INSPIRE].
P. de Forcrand and O. Philipsen, The Chiral critical point of N(f) = 3 QCD at finite density to the order (mu/T)**4, JHEP 11 (2008) 012 [arXiv:0808.1096] [INSPIRE].
M. D’Elia and M.-P. Lombardo, Finite density QCD via imaginary chemical potential, Phys. Rev. D 67 (2003) 014505 [hep-lat/0209146] [INSPIRE].
M. D’Elia and M.P. Lombardo, QCD thermodynamics from an imaginary mu(B): Results on the four flavor lattice model, Phys. Rev. D 70 (2004) 074509 [hep-lat/0406012] [INSPIRE].
V. Azcoiti, G. Di Carlo, A. Galante and V. Laliena, Phase diagram of QCD with four quark flavors at finite temperature and baryon density, Nucl. Phys. B 723 (2005) 77 [hep-lat/0503010] [INSPIRE].
H.-S. Chen and X.-Q. Luo, Phase diagram of QCD at finite temperature and chemical potential from lattice simulations with dynamical Wilson quarks, Phys. Rev. D 72 (2005) 034504 [hep-lat/0411023] [INSPIRE].
F. Karbstein and M. Thies, How to get from imaginary to real chemical potential, Phys. Rev. D 75 (2007) 025003 [hep-th/0610243] [INSPIRE].
P. Cea, L. Cosmai, M. D’Elia and A. Papa, Analytic continuation from imaginary to real chemical potential in two-color QCD, JHEP 02 (2007) 066 [hep-lat/0612018] [INSPIRE].
P. Cea, L. Cosmai, M. D’Elia and A. Papa, The Critical line from imaginary to real baryonic chemical potentials in two-color QCD, Phys. Rev. D 77 (2008) 051501 [arXiv:0712.3755] [INSPIRE].
P. Cea, L. Cosmai, M. D’Elia and A. Papa, The phase diagram of QCD with four degenerate quarks, Phys. Rev. D 81 (2010) 094502 [arXiv:1004.0184] [INSPIRE].
L.-K. Wu, X.-Q. Luo and H.-S. Chen, Phase structure of lattice QCD with two flavors of Wilson quarks at finite temperature and chemical potential, Phys. Rev. D 76 (2007) 034505 [hep-lat/0611035] [INSPIRE].
K. Nagata and A. Nakamura, Imaginary Chemical Potential Approach for the Pseudo-Critical Line in the QCD Phase Diagram with Clover-Improved Wilson Fermions, Phys. Rev. D 83 (2011) 114507 [arXiv:1104.2142] [INSPIRE].
P. Giudice and A. Papa, Real and imaginary chemical potential in two color QCD, Phys. Rev. D 69 (2004) 094509 [hep-lat/0401024] [INSPIRE].
M. D’Elia, F. Di Renzo and M.P. Lombardo, The Strongly interacting quark gluon plasma and the critical behaviour of QCD at imaginary mu, Phys. Rev. D 76 (2007) 114509 [arXiv:0705.3814] [INSPIRE].
P. Cea, L. Cosmai, M. D’Elia, C. Manneschi and A. Papa, Analytic continuation of the critical line: Suggestions for QCD, Phys. Rev. D 80 (2009) 034501 [arXiv:0905.1292] [INSPIRE].
A. Alexandru and A. Li, QCD at imaginary chemical potential with Wilson fermions, PoS(LATTICE2013)208 (2014) [arXiv:1312.1201] [INSPIRE].
P. Cea, L. Cosmai, M. D’Elia, A. Papa and F. Sanfilippo, The critical line of two-flavor QCD at finite isospin or baryon densities from imaginary chemical potentials, Phys. Rev. D 85 (2012) 094512 [arXiv:1202.5700] [INSPIRE].
S. Conradi and M. D’Elia, Imaginary chemical potentials and the phase of the fermionic determinant, Phys. Rev. D 76 (2007) 074501 [arXiv:0707.1987] [INSPIRE].
M. D’Elia and F. Sanfilippo, Thermodynamics of two flavor QCD from imaginary chemical potentials, Phys. Rev. D 80 (2009) 014502 [arXiv:0904.1400] [INSPIRE].
T. Takaishi, P. de Forcrand and A. Nakamura, Equation of State at Finite Density from Imaginary Chemical Potential, PoS(LAT2009)198 (2009) [arXiv:1002.0890] [INSPIRE].
P. Cea, L. Cosmai and A. Papa, Critical line of 2 + 1 flavor QCD, Phys. Rev. D 89 (2014) 074512 [arXiv:1403.0821] [INSPIRE].
P. Cea, L. Cosmai and A. Papa, Critical line of 2 + 1 flavor QCD: Toward the continuum limit, Phys. Rev. D 93 (2016) 014507 [arXiv:1508.07599] [INSPIRE].
C. Bonati, P. de Forcrand, M. D’Elia, O. Philipsen and F. Sanfilippo, Chiral phase transition in two-flavor QCD from an imaginary chemical potential, Phys. Rev. D 90 (2014) 074030 [arXiv:1408.5086] [INSPIRE].
C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro and F. Sanfilippo, Curvature of the chiral pseudocritical line in QCD, Phys. Rev. D 90 (2014) 114025 [arXiv:1410.5758] [INSPIRE].
C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro and F. Sanfilippo, Curvature of the chiral pseudocritical line in QCD: Continuum extrapolated results, Phys. Rev. D 92 (2015) 054503 [arXiv:1507.03571] [INSPIRE].
R. Bellwied et al., The QCD phase diagram from analytic continuation, Phys. Lett. B 751 (2015) 559 [arXiv:1507.07510] [INSPIRE].
J.N. Guenther et al., The QCD equation of state at finite density from analytical continuation, Nucl. Phys. A 967 (2017) 720 [arXiv:1607.02493] [INSPIRE].
M. D’Elia, G. Gagliardi and F. Sanfilippo, Higher order quark number fluctuations via imaginary chemical potentials in N f = 2 + 1 QCD, Phys. Rev. D 95 (2017) 094503 [arXiv:1611.08285] [INSPIRE].
V.G. Bornyakov et al., Lattice QCD at finite baryon density using analytic continuation, EPJ Web Conf. 182 (2018) 02017 [arXiv:1712.02830] [INSPIRE].
M. Andreoli et al., Gauge-invariant screening masses and static quark free energies in N f = 2 + 1 QCD at nonzero baryon density, Phys. Rev. D 97 (2018) 054515 [arXiv:1712.09996] [INSPIRE].
J. Greensite and K. Langfeld, Finding the effective Polyakov line action for SU(3) gauge theories at finite chemical potential, Phys. Rev. D 90 (2014) 014507 [arXiv:1403.5844] [INSPIRE].
J. Greensite, Comparison of complex Langevin and mean field methods applied to effective Polyakov line models, Phys. Rev. D 90 (2014) 114507 [arXiv:1406.4558] [INSPIRE].
J. Takahashi, H. Kouno and M. Yahiro, Quark number densities at imaginary chemical potential in N f = 2 lattice QCD with Wilson fermions and its model analyses, Phys. Rev. D 91 (2015) 014501 [arXiv:1410.7518] [INSPIRE].
J. Takahashi, J. Sugano, M. Ishii, H. Kouno and M. Yahiro, Quark number density at imaginary chemical potential and its extrapolation to large real chemical potential by the effective model, PoS(LATTICE2014)187 (2015) [arXiv:1410.8279] [INSPIRE].
J. Greensite and R. Höllwieser, Finite-density transition line for QCD with 695 MeV dynamical fermions, Phys. Rev. D 97 (2018) 114504 [arXiv:1708.08031] [INSPIRE].
M. D’Elia and F. Sanfilippo, The Order of the Roberge-Weiss endpoint (finite size transition) in QCD, Phys. Rev. D 80 (2009) 111501 [arXiv:0909.0254] [INSPIRE].
P. de Forcrand and O. Philipsen, Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential, Phys. Rev. Lett. 105 (2010) 152001 [arXiv:1004.3144] [INSPIRE].
C. Bonati, G. Cossu, M. D’Elia and F. Sanfilippo, The Roberge-Weiss endpoint in N f = 2 QCD, Phys. Rev. D 83 (2011) 054505 [arXiv:1011.4515] [INSPIRE].
O. Philipsen and C. Pinke, Nature of the Roberge-Weiss transition in N f = 2 QCD with Wilson fermions, Phys. Rev. D 89 (2014) 094504 [arXiv:1402.0838] [INSPIRE].
L.-K. Wu and X.-F. Meng, Nature of the Roberge-Weiss transition end points in two-flavor lattice QCD with Wilson quarks, Phys. Rev. D 87 (2013) 094508 [arXiv:1303.0336] [INSPIRE].
L.-K. Wu and X.-F. Meng, Nature of Roberge-Weiss transition endpoints for heavy quarks in N f = 2 lattice QCD with Wilson fermions, Phys. Rev. D 90 (2014) 094506 [arXiv:1405.2425] [INSPIRE].
K. Nagata, K. Kashiwa, A. Nakamura and S.M. Nishigaki, Lee-Yang zero distribution of high temperature QCD and the Roberge-Weiss phase transition, Phys. Rev. D 91 (2015) 094507 [arXiv:1410.0783] [INSPIRE].
K. Kashiwa and A. Ohnishi, Quark number holonomy and confinement-deconfinement transition, Phys. Rev. D 93 (2016) 116002 [arXiv:1602.06037] [INSPIRE].
K. Kashiwa and A. Ohnishi, Topological feature and phase structure of QCD at complex chemical potential, Phys. Lett. B 750 (2015) 282 [arXiv:1505.06799] [INSPIRE].
C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro and F. Sanfilippo, Roberge-Weiss endpoint at the physical point of N f = 2 + 1 QCD, Phys. Rev. D 93 (2016) 074504 [arXiv:1602.01426] [INSPIRE].
T. Makiyama et al., Phase structure of two-color QCD at real and imaginary chemical potentials; lattice simulations and model analyses, Phys. Rev. D 93 (2016) 014505 [arXiv:1502.06191] [INSPIRE].
C. Pinke and O. Philipsen, The N f = 2 chiral phase transition from imaginary chemical potential with Wilson Fermions, PoS(LATTICE2015)149 (2016) [arXiv:1508.07725] [INSPIRE].
C. Czaban, F. Cuteri, O. Philipsen, C. Pinke and A. Sciarra, Roberge-Weiss transition in N f = 2 QCD with Wilson fermions and N τ = 6, Phys. Rev. D 93 (2016) 054507 [arXiv:1512.07180] [INSPIRE].
C. Bonati et al., Roberge-Weiss endpoint and chiral symmetry restoration in N f = 2 + 1 QCD, Phys. Rev. D 99 (2019) 014502 [arXiv:1807.02106] [INSPIRE].
H. Kouno, Y. Sakai, K. Kashiwa and M. Yahiro, Roberge-Weiss phase transition and its endpoint, J. Phys. G 36 (2009) 115010 [arXiv:0904.0925] [INSPIRE].
Y. Sakai, K. Kashiwa, H. Kouno, M. Matsuzaki and M. Yahiro, Determination of QCD phase diagram from the imaginary chemical potential region, Phys. Rev. D 79 (2009) 096001 [arXiv:0902.0487] [INSPIRE].
T. Sasaki, Y. Sakai, H. Kouno and M. Yahiro, Quark-mass dependence of the three-flavor QCD phase diagram at zero and imaginary chemical potential: Model prediction, Phys. Rev. D 84 (2011) 091901 [arXiv:1105.3959] [INSPIRE].
H. Kouno, M. Kishikawa, T. Sasaki, Y. Sakai and M. Yahiro, Spontaneous parity and charge-conjugation violations at real isospin and imaginary baryon chemical potentials, Phys. Rev. D 85 (2012) 016001 [arXiv:1110.5187] [INSPIRE].
G. Aarts, S.P. Kumar and J. Rafferty, Holographic Roberge-Weiss Transitions, JHEP 07 (2010) 056 [arXiv:1005.2947] [INSPIRE].
J. Rafferty, Holographic Roberge Weiss Transitions II — Defect Theories and the Sakai Sugimoto Model, JHEP 09 (2011) 087 [arXiv:1103.2315] [INSPIRE].
K. Morita, V. Skokov, B. Friman and K. Redlich, Probing deconfinement in a chiral effective model with Polyakov loop at imaginary chemical potential, Phys. Rev. D 84 (2011) 076009 [arXiv:1107.2273] [INSPIRE].
K. Kashiwa, T. Hell and W. Weise, Nonlocal Polyakov-Nambu-Jona-Lasinio model and imaginary chemical potential, Phys. Rev. D 84 (2011) 056010 [arXiv:1106.5025] [INSPIRE].
V. Pagura, D. Gomez Dumm and N.N. Scoccola, Deconfinement and chiral restoration in nonlocal PNJL models at zero and imaginary chemical potential, Phys. Lett. B 707 (2012) 76 [arXiv:1105.1739] [INSPIRE].
D. Scheffler, M. Buballa and J. Wambach, PNJL Model Analysis of the Roberge-Weiss Transition Endpoint at Imaginary Chemical Potential, Acta Phys. Polon. Supp. 5 (2012) 971 [arXiv:1111.3839] [INSPIRE].
K. Kashiwa and R.D. Pisarski, Roberge-Weiss transition and ’t Hooft loops, Phys. Rev. D 87 (2013) 096009 [arXiv:1301.5344] [INSPIRE].
K. Kashiwa, T. Sasaki, H. Kouno and M. Yahiro, Two-color QCD at imaginary chemical potential and its impact on real chemical potential, Phys. Rev. D 87 (2013) 016015 [arXiv:1208.2283] [INSPIRE].
E.G. Filothodoros, A.C. Petkou and N.D. Vlachos, 3d fermion-boson map with imaginary chemical potential, Phys. Rev. D 95 (2017) 065029 [arXiv:1608.07795] [INSPIRE].
E.G. Filothodoros, A.C. Petkou and N.D. Vlachos, The fermion-boson map for large d, Nucl. Phys. B 941 (2019) 195 [arXiv:1803.05950] [INSPIRE].
A. Roberge and N. Weiss, Gauge Theories With Imaginary Chemical Potential and the Phases of QCD, Nucl. Phys. B 275 (1986) 734 [INSPIRE].
H. Kouno, Y. Sakai, T. Makiyama, K. Tokunaga, T. Sasaki and M. Yahiro, quark-gluon thermodynamics with the Z(N(c)) symmetry, J. Phys. G 39 (2012) 085010 [INSPIRE].
Y. Sakai, H. Kouno, T. Sasaki and M. Yahiro, The quarkyonic phase and the \( {Z}_{N_c} \) symmetry, Phys. Lett. B 718 (2012) 130 [arXiv:1204.0228] [INSPIRE].
H. Kouno, T. Makiyama, T. Sasaki, Y. Sakai and M. Yahiro, Confinement and ℤ3 symmetry in three-flavor QCD, J. Phys. G 40 (2013) 095003 [arXiv:1301.4013] [INSPIRE].
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. D 88 (2013) 016002 [arXiv:1304.3274] [INSPIRE].
E. Poppitz and T. Sulejmanpasic, (S)QCD on \( {\mathbb{R}}^3 \times {\mathbb{S}}^1 \) : Screening of Polyakov loop by fundamental quarks and the demise of semi-classics, JHEP 09 (2013) 128 [arXiv:1307.1317] [INSPIRE].
T. Iritani, E. Itou and T. Misumi, Lattice study on QCD-like theory with exact center symmetry, JHEP 11 (2015) 159 [arXiv:1508.07132] [INSPIRE].
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. D 93 (2016) 056009 [arXiv:1504.07585] [INSPIRE].
T. Hirakida, H. Kouno, J. Takahashi and M. Yahiro, Interplay between sign problem and Z 3 symmetry in three-dimensional Potts models, Phys. Rev. D 94 (2016) 014011 [arXiv:1604.02977] [INSPIRE].
T. Hirakida, J. Sugano, H. Kouno, J. Takahashi and M. Yahiro, Sign problem in Z 3 -symmetric effective Polyakov-line model, Phys. Rev. D 96 (2017) 074031 [arXiv:1705.00665] [INSPIRE].
A. Cherman, S. Sen, M. Ünsal, M.L. Wagman and L.G. Yaffe, Order parameters and color-flavor center symmetry in QCD, Phys. Rev. Lett. 119 (2017) 222001 [arXiv:1706.05385] [INSPIRE].
A.N. Redlich, Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions, Phys. Rev. D 29 (1984) 2366 [INSPIRE].
A.J. Niemi and G.W. Semenoff, Axial Anomaly Induced Fermion Fractionization and Effective Gauge Theory Actions in Odd Dimensional Space-Times, Phys. Rev. Lett. 51 (1983)2077 [INSPIRE].
L. Álvarez-Gaumé, S. Della Pietra and G.W. Moore, Anomalies and Odd Dimensions, Annals Phys. 163 (1985) 288 [INSPIRE].
E. Witten, The “Parity” Anomaly On An Unorientable Manifold, Phys. Rev. B 94 (2016) 195150 [arXiv:1605.02391] [INSPIRE].
E. Witten, Global Aspects of Current Algebra, Nucl. Phys. B 223 (1983) 422 [INSPIRE].
E. Witten, Current Algebra, Baryons and Quark Confinement, Nucl. Phys. B 223 (1983) 433 [INSPIRE].
M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian Geometry 1, Math. Proc. Cambridge Phil. Soc. 77 (1975) 43 [INSPIRE].
H. Fukaya, T. Onogi and S. Yamaguchi, Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator, Phys. Rev. D 96 (2017) 125004 [arXiv:1710.03379] [INSPIRE].
M. Bando, T. Kugo, S. Uehara, K. Yamawaki and T. Yanagida, Is rho Meson a Dynamical Gauge Boson of Hidden Local Symmetry?, Phys. Rev. Lett. 54 (1985) 1215 [INSPIRE].
D.S. Freed and M.J. Hopkins, Reflection positivity and invertible topological phases, arXiv:1604.06527 [INSPIRE].
K. Yonekura, On the cobordism classification of symmetry protected topological phases, arXiv:1803.10796 [INSPIRE].
E. Witten, Fermion Path Integrals And Topological Phases, Rev. Mod. Phys. 88 (2016) 035001 [arXiv:1508.04715] [INSPIRE].
K. Yonekura, Dai-Freed theorem and topological phases of matter, JHEP 09 (2016) 022 [arXiv:1607.01873] [INSPIRE].
Z. Komargodski, A. Sharon, R. Thorngren and X. Zhou, Comments on Abelian Higgs Models and Persistent Order, SciPost Phys. 6 (2019) 003 [arXiv:1705.04786] [INSPIRE].
E. Witten, Baryons in the 1/n Expansion, Nucl. Phys. B 160 (1979) 57 [INSPIRE].
M. Hanada, G. Ishiki and H. Watanabe, Partial Deconfinement, JHEP 03 (2019) 145 [arXiv:1812.05494] [INSPIRE].
N. Seiberg and E. Witten, Gapped Boundary Phases of Topological Insulators via Weak Coupling, PTEP 2016 (2016) 12C101 [arXiv:1602.04251] [INSPIRE].
Y. Tachikawa and K. Yonekura, On time-reversal anomaly of 2 + 1d topological phases, PTEP 2017 (2017) 033B04 [arXiv:1610.07010] [INSPIRE].
Y. Tachikawa and K. Yonekura, More on time-reversal anomaly of 2 + 1d topological phases, Phys. Rev. Lett. 119 (2017) 111603 [arXiv:1611.01601] [INSPIRE].
J. Wang, X.-G. Wen and E. Witten, Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions, Phys. Rev. X 8 (2018) 031048 [arXiv:1705.06728] [INSPIRE].
I. García-Etxebarria, H. Hayashi, K. Ohmori, Y. Tachikawa and K. Yonekura, 8d gauge anomalies and the topological Green-Schwarz mechanism, JHEP 11 (2017) 177 [arXiv:1710.04218] [INSPIRE].
Y. Tachikawa, On gauging finite subgroups, arXiv:1712.09542 [INSPIRE].
J. Wang et al., Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions, PTEP 2018 (2018) 053A01 [arXiv:1801.05416] [INSPIRE].
Y. Lee and Y. Tachikawa, A study of time reversal symmetry of abelian anyons, JHEP 07 (2018) 090 [arXiv:1805.02738] [INSPIRE].
C.-T. Hsieh, Discrete gauge anomalies revisited, arXiv:1808.02881 [INSPIRE].
K.A. Intriligator and N. Seiberg, Lectures on supersymmetric gauge theories and electric-magnetic duality, Nucl. Phys. Proc. Suppl. 45BC (1996) 1 [hep-th/9509066] [INSPIRE].
V. Borokhov, A. Kapustin and X.-k. Wu, Topological disorder operators in three-dimensional conformal field theory, JHEP 11 (2002) 049 [hep-th/0206054] [INSPIRE].
S.S. Pufu, Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics, Phys. Rev. D 89 (2014) 065016 [arXiv:1303.6125] [INSPIRE].
O. Aharony, J. Sonnenschein and S. Yankielowicz, A Holographic model of deconfinement and chiral symmetry restoration, Annals Phys. 322 (2007) 1420 [hep-th/0604161] [INSPIRE].
G. Mandal and T. Morita, Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD, JHEP 09 (2011) 073 [arXiv:1107.4048] [INSPIRE].
H. Isono, G. Mandal and T. Morita, Thermodynamics of QCD from Sakai-Sugimoto Model, JHEP 12 (2015) 006 [arXiv:1507.08949] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
E. Witten, Current Algebra Theorems for the U(1) Goldstone Boson, Nucl. Phys. B 156 (1979) 269 [INSPIRE].
E. Witten, Large N Chiral Dynamics, Annals Phys. 128 (1980) 363 [INSPIRE].
E. Witten, Theta dependence in the large N limit of four-dimensional gauge theories, Phys. Rev. Lett. 81 (1998) 2862 [hep-th/9807109] [INSPIRE].
K. Yonekura, Notes on natural inflation, JCAP 10 (2014) 054 [arXiv:1405.0734] [INSPIRE].
M. Panero, Thermodynamics of the QCD plasma and the large-N limit, Phys. Rev. Lett. 103 (2009) 232001 [arXiv:0907.3719] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1901.08188
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Yonekura, K. Anomaly matching in QCD thermal phase transition. J. High Energ. Phys. 2019, 62 (2019). https://doi.org/10.1007/JHEP05(2019)062
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2019)062