Abstract
We study the bilinear and higher-order fermion condensates in 4-dimensional SU(N) gauge theories with a single Dirac fermion in a general representation. Augmented with a mixed anomaly between the 0-form discrete chiral, 1-form center, and 0-form baryon number symmetries (BC anomaly), we sort out theories that admit higher-order condensates and vanishing fermion bilinears. Then, the BC anomaly is utilized to prove, in the absence of a topological quantum field theory, that nonvanishing fermion bilinears are inevitable in infrared-gapped theories with 2-index (anti)symmetric fermions. We also contrast the BC anomaly with the 0-form anomalies and show that it is the former anomaly that determines the infrared physics; we argue that the BC anomaly lurks deep to the infrared while the 0-form anomalies are just variations of local terms. We provide evidence of this assertion by studying the BC anomaly in vector-like theories compactified on a small spacial circle. These theories are weakly-coupled, under analytical control, and they admit a dual description in terms of abelian photons that determine the deep infrared dynamics. We show that the dual photons talk directly to the 1-form center symmetry in order to match the BC anomaly, while the 0-form anomalies are variations of local terms and are matched by fiat. Finally, we study the fate of the BC anomaly in the compactified theories when they are held at a finite temperature. The effective field theory that describes the low-energy physics is 2-dimensional. We show that the BC anomaly cascades from 4 to 2 dimensions.
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References
G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Sci. Ser. B 59 (1980) 135 [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized global symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, Theta, time reversal and temperature, JHEP 05 (2017) 091 [arXiv:1703.00501] [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].
T. Sulejmanpasic and Y. Tanizaki, C-P-T anomaly matching in bosonic quantum field theory and spin chains, Phys. Rev. B 97 (2018) 144201 [arXiv:1802.02153] [INSPIRE].
Z. Wan and J. Wang, Higher anomalies, higher symmetries, and cobordisms I: classification of higher-symmetry-protected topological states and their boundary fermionic/bosonic anomalies via a generalized cobordism theory, Ann. Math. Sci. Appl. 4 (2019) 107 [arXiv:1812.11967] [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the space of coupling constants and their dynamical applications I, SciPost Phys. 8 (2020) 001 [arXiv:1905.09315] [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the space of coupling constants and their dynamical applications II, SciPost Phys. 8 (2020) 002 [arXiv:1905.13361] [INSPIRE].
M.M. Anber, Self-conjugate QCD, JHEP 10 (2019) 042 [arXiv:1906.10315] [INSPIRE].
C. Córdova and K. Ohmori, Anomaly constraints on gapped phases with discrete chiral symmetry, Phys. Rev. D 102 (2020) 025011 [arXiv:1912.13069] [INSPIRE].
M.M. Anber and S. Baker, Natural inflation, strong dynamics, and the role of generalized anomalies, Phys. Rev. D 102 (2020) 103515 [arXiv:2008.05491] [INSPIRE].
C. Córdova and T.T. Dumitrescu, Candidate phases for SU(2) adjoint QCD4 with two flavors from N = 2 supersymmetric Yang-Mills theory, arXiv:1806.09592 [INSPIRE].
M.M. Anber and E. Poppitz, Two-flavor adjoint QCD, Phys. Rev. D 98 (2018) 034026 [arXiv:1805.12290] [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].
M.M. Anber and E. Poppitz, Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj), JHEP 05 (2019) 151 [arXiv:1811.10642] [INSPIRE].
M. Ünsal, Strongly coupled QFT dynamics via TQFT coupling, arXiv:2007.03880 [INSPIRE].
T. Sulejmanpasic, Y. Tanizaki and M. Ünsal, Universality between vector-like and chiral quiver gauge theories: anomalies and domain walls, JHEP 06 (2020) 173 [arXiv:2004.10328] [INSPIRE].
Y. Tanizaki and M. Ünsal, Modified instanton sum in QCD and higher-groups, JHEP 03 (2020) 123 [arXiv:1912.01033] [INSPIRE].
A. Cherman and T. Jacobson, Lifetimes of (near) eternal false vacua, arXiv:2012.10555 [INSPIRE].
A. Cherman, T. Jacobson, Y. Tanizaki and M. Ünsal, Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD, SciPost Phys. 8 (2020) 072 [arXiv:1908.09858] [INSPIRE].
H. Shimizu and K. Yonekura, Anomaly constraints on deconfinement and chiral phase transition, Phys. Rev. D 97 (2018) 105011 [arXiv:1706.06104] [INSPIRE].
T.D. Brennan and C. Cordova, Axions, higher-groups, and emergent symmetry, arXiv:2011.09600 [INSPIRE].
G. ’t Hooft, A property of electric and magnetic flux in non-Abelian gauge theories, Nucl. Phys. B 153 (1979) 141 [INSPIRE].
P. van Baal, Some results for SU(N) gauge fields on the hypertorus, Commun. Math. Phys. 85 (1982) 529 [INSPIRE].
M.M. Anber and E. Poppitz, On the baryon-color-flavor (BCF) anomaly in vector-like theories, JHEP 11 (2019) 063 [arXiv:1909.09027] [INSPIRE].
M.M. Anber and E. Poppitz, Generalized ’t Hooft anomalies on non-spin manifolds, JHEP 04 (2020) 097 [arXiv:2002.02037] [INSPIRE].
E. Poppitz and F.D. Wandler, Topological terms and anomaly matching in effective field theories on ℝ3 × \( {\mathbbm{S}}^1 \). Part I. Abelian symmetries and intermediate scales, JHEP 01 (2021) 091 [arXiv:2009.14667] [INSPIRE].
M.M. Anber and E. Poppitz, Deconfinement on axion domain walls, JHEP 03 (2020) 124 [arXiv:2001.03631] [INSPIRE].
A. Kapustin and N. Seiberg, Coupling a QFT to a TQFT and duality, JHEP 04 (2014) 001 [arXiv:1401.0740] [INSPIRE].
C. Córdova and K. Ohmori, Anomaly obstructions to symmetry preserving gapped phases, arXiv:1910.04962 [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 L. Vincent-Genod, Classification of compactified su(Nc) gauge theories with fermions in all representations, JHEP 12 (2017) 028 [arXiv:1704.08277] [INSPIRE].
G.V. Dunne and M. Ünsal, New nonperturbative methods in quantum field theory: from large-N orbifold equivalence to bions and resurgence, Ann. Rev. Nucl. Part. Sci. 66 (2016) 245 [arXiv:1601.03414] [INSPIRE].
D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and instantons at finite temperature, Rev. Mod. Phys. 53 (1981) 43 [INSPIRE].
C. Callias, Index theorems on open spaces, Commun. Math. Phys. 62 (1978) 213 [INSPIRE].
E. Poppitz and M. Ünsal, Index theorem for topological excitations on R3 × S1 and Chern-Simons theory, JHEP 03 (2009) 027 [arXiv:0812.2085] [INSPIRE].
M.M. Anber, E. Poppitz and B. Teeple, Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups, JHEP 09 (2014) 040 [arXiv:1406.1199] [INSPIRE].
N.M. Davies, T.J. Hollowood and V.V. Khoze, Monopoles, affine algebras and the gluino condensate, J. Math. Phys. 44 (2003) 3640 [hep-th/0006011] [INSPIRE].
P.C. Argyres and M. Ünsal, The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects, JHEP 08 (2012) 063 [arXiv:1206.1890] [INSPIRE].
M. Ünsal, Magnetic bion condensation: a new mechanism of confinement and mass gap in four dimensions, Phys. Rev. D 80 (2009) 065001 [arXiv:0709.3269] [INSPIRE].
M.M. Anber and E. Poppitz, Microscopic structure of magnetic bions, JHEP 06 (2011) 136 [arXiv:1105.0940] [INSPIRE].
E. Poppitz and M. Ünsal, Conformality or confinement: (IR)relevance of topological excitations, JHEP 09 (2009) 050 [arXiv:0906.5156] [INSPIRE].
E. Poppitz, T. Schäfer and M. Ünsal, Continuity, deconfinement, and (super) Yang-Mills theory, JHEP 10 (2012) 115 [arXiv:1205.0290] [INSPIRE].
M.M. Anber, E. Poppitz and M. Ünsal, 2d affine XY-spin model/4d gauge theory duality and deconfinement, JHEP 04 (2012) 040 [arXiv:1112.6389] [INSPIRE].
M.M. Anber, S. Collier and E. Poppitz, The SU(3)/ℤ3 QCD(adj) deconfinement transition via the gauge theory/“affine” XY-model duality, JHEP 01 (2013) 126 [arXiv:1211.2824] [INSPIRE].
M.M. Anber, The Abelian confinement mechanism revisited: new aspects of the Georgi-Glashow model, Annals Phys. 341 (2014) 21 [arXiv:1308.0027] [INSPIRE].
M.M. Anber, S. Collier, E. Poppitz, S. Strimas-Mackey and B. Teeple, Deconfinement in N = 1 super Yang-Mills theory on ℝ3 × \( {\mathbbm{S}}^1 \) via dual-Coulomb gas and “affine” XY-model, JHEP 11 (2013) 142 [arXiv:1310.3522] [INSPIRE].
M.M. Anber and B.J. Kolligs, Entanglement entropy, dualities, and deconfinement in gauge theories, JHEP 08 (2018) 175 [arXiv:1804.01956] [INSPIRE].
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Anber, M.M. Condensates and anomaly cascade in vector-like theories. J. High Energ. Phys. 2021, 191 (2021). https://doi.org/10.1007/JHEP03(2021)191
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DOI: https://doi.org/10.1007/JHEP03(2021)191