Abstract
We explore the idea that in some class of strongly-coupled chiral SU(N) gauge theories the infrared dynamics might be characterized by a bifermion condensate in the ad- joint representation of the color gauge group. As an illustration, in this work we revisit an SU(N) chiral gauge theory with Weyl fermions in a symmetric (ψ) and anti-antisymmetric (χ) tensor representations, together with eight fermions in the anti-fundamental representations (η), which we called ψχη model in the previous investigations. We study the infrared dynamics of this system more carefully, by assuming dynamical Abelianization, a phenomenon familiar from 𝒩 = 2 supersymmetric gauge theories, and by analyzing the way various continuous and discrete symmetries are realized at low energies. We submit then these ideas to a more stringent test, by taking into account some higher-form symmetries and the consequent mixed anomalies. A detailed analysis of the mixed anomalies involving certain 0-form U(1) symmetries and the color-flavor locked 1-form ℤN symmetry in the ψχη system shows that the proposed infrared dynamics is consistent with it.
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S. Raby, S. Dimopoulos and L. Susskind, Tumbling gauge theories, Nucl. Phys. B 169 (1980) 373 [INSPIRE].
S. Dimopoulos, S. Raby and L. Susskind, Light composite fermions, Nucl. Phys. B 173 (1980) 208 [INSPIRE].
I. Bars and S. Yankielowicz, Composite quarks and leptons as solutions of anomaly constraints, Phys. Lett. B 101 (1981) 159 [INSPIRE].
G. Veneziano, Tumbling and the strong anomaly, Phys. Lett. B 102 (1981) 139 [INSPIRE].
J. Goity, R.D. Peccei and D. Zeppenfeld, Tumbling and complementarity in a chiral gauge theory, Nucl. Phys. B 262 (1985) 95 [INSPIRE].
E. Eichten, R.D. Peccei, J. Preskill and D. Zeppenfeld, Chiral gauge theories in the 1/n expansion, Nucl. Phys. B 268 (1986) 161 [INSPIRE].
C.Q. Geng and R.E. Marshak, Two realistic preon models with SU(N) metacolor satisfying complementarity, Phys. Rev. D 35 (1987) 2278 [INSPIRE].
T. Appelquist, A.G. Cohen, M. Schmaltz and R. Shrock, New constraints on chiral gauge theories, Phys. Lett. B 459 (1999) 235 [hep-th/9904172] [INSPIRE].
T. Appelquist, Z.-Y. Duan and F. Sannino, Phases of chiral gauge theories, Phys. Rev. D 61 (2000) 125009 [hep-ph/0001043] [INSPIRE].
M. Shifman and M. Ünsal, On Yang-Mills theories with chiral matter at strong coupling, Phys. Rev. D 79 (2009) 105010 [arXiv:0808.2485] [INSPIRE].
E. Poppitz and Y. Shang, Chiral lattice gauge theories via mirror-fermion decoupling: a mission (im)possible?, Int. J. Mod. Phys. A 25 (2010) 2761 [arXiv:1003.5896] [INSPIRE].
A. Armoni and M. Shifman, A chiral SU(N) gauge theory planar equivalent to super-Yang-Mills, Phys. Rev. D 85 (2012) 105003 [arXiv:1202.1657] [INSPIRE].
Y.-L. Shi and R. Shrock, AkF chiral gauge theories, Phys. Rev. D 92 (2015) 105032 [arXiv:1510.07663] [INSPIRE].
Y.-L. Shi and R. Shrock, Renormalization-group evolution and nonperturbative behavior of chiral gauge theories with fermions in higher-dimensional representations, Phys. Rev. D 92 (2015) 125009 [arXiv:1509.08501] [INSPIRE].
S. Bolognesi, K. Konishi and M. Shifman, Patterns of symmetry breaking in chiral QCD, Phys. Rev. D 97 (2018) 094007 [arXiv:1712.04814] [INSPIRE].
S. Bolognesi and K. Konishi, Dynamics and symmetries in chiral SU(N) gauge theories, Phys. Rev. D 100 (2019) 114008 [arXiv:1906.01485] [INSPIRE].
S. Bolognesi, K. Konishi and A. Luzio, Gauging 1-form center symmetries in simple SU(N) gauge theories, JHEP 01 (2020) 048 [arXiv:1909.06598] [INSPIRE].
S. Bolognesi, K. Konishi and A. Luzio, Dynamics from symmetries in chiral SU(N) gauge theories, JHEP 09 (2020) 001 [arXiv:2004.06639] [INSPIRE].
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].
H. Shimizu and K. Yonekura, Anomaly constraints on deconfinement and chiral phase transition, Phys. Rev. D 97 (2018) 105011 [arXiv:1706.06104] [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].
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].
Y. Tanizaki, Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking, JHEP 08 (2018) 171 [arXiv:1807.07666] [INSPIRE].
S. Yamaguchi, ’t Hooft anomaly matching condition and chiral symmetry breaking without bilinear condensate, JHEP 01 (2019) 014 [arXiv:1811.09390] [INSPIRE].
A. Karasik and Z. Komargodski, The bi-fundamental gauge theory in 3 + 1 dimensions: the vacuum structure and a cascade, JHEP 05 (2019) 144 [arXiv:1904.09551] [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].
C. Córdova and K. Ohmori, Anomaly obstructions to symmetry preserving gapped phases, arXiv:1910.04962 [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].
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].
Z. Wan and J. Wang, Adjoint QCD4, deconfined critical phenomena, symmetry-enriched topological quantum field theory, and higher symmetry-extension, Phys. Rev. D 99 (2019) 065013 [arXiv:1812.11955] [INSPIRE].
S. Bolognesi, K. Konishi and A. Luzio, Probing the dynamics of chiral SU(N) gauge theories via generalized anomalies, Phys. Rev. D 103 (2021) 094016 [arXiv:2101.02601] [INSPIRE].
P.B. Smith, A. Karasik, N. Lohitsiri and D. Tong, On discrete anomalies in chiral gauge theories, JHEP 01 (2022) 112 [arXiv:2106.06402] [INSPIRE].
M.M. Anber, S. Hong and M. Son, New anomalies, TQFTs, and confinement in bosonic chiral gauge theories, JHEP 02 (2022) 062 [arXiv:2109.03245] [INSPIRE].
S. Bolognesi, K. Konishi and A. Luzio, Strong anomaly and phases of chiral gauge theories, JHEP 08 (2021) 028 [arXiv:2105.03921] [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. 430 (1994) 485] [hep-th/9407087] [INSPIRE].
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].
Y. Tachikawa, N = 2 supersymmetric dynamics for pedestrians, Lect. Notes Phys. 890 (2014) 1 [arXiv:1312.2684] [INSPIRE].
F. Ferrari and A. Bilal, The strong coupling spectrum of the Seiberg-Witten theory, Nucl. Phys. B 469 (1996) 387 [hep-th/9602082] [INSPIRE].
A. Cappelli, P. Valtancoli and L. Vergnano, Isomonodromic properties of the Seiberg-Witten solution, Nucl. Phys. B 524 (1998) 469 [hep-th/9710248] [INSPIRE].
A. Ritz, M.A. Shifman, A.I. Vainshtein and M.B. Voloshin, Marginal stability and the metamorphosis of BPS states, Phys. Rev. D 63 (2001) 065018 [hep-th/0006028] [INSPIRE].
E. Witten, Current algebra theorems for the U(1) Goldstone boson, Nucl. Phys. B 156 (1979) 269 [INSPIRE].
G. Veneziano, U(1) without instantons, Nucl. Phys. B 159 (1979) 213 [INSPIRE].
C. Rosenzweig, J. Schechter and C.G. Trahern, Is the effective Lagrangian for QCD a sigma model?, Phys. Rev. D 21 (1980) 3388 [INSPIRE].
P. Di Vecchia and G. Veneziano, Chiral dynamics in the large N limit, Nucl. Phys. B 171 (1980) 253 [INSPIRE].
E. Witten, Large N chiral dynamics, Annals Phys. 128 (1980) 363 [INSPIRE].
K. Kawarabayashi and N. Ohta, The problem of η in the large N limit: effective Lagrangian approach, Nucl. Phys. B 175 (1980) 477 [INSPIRE].
P. Nath and R.L. Arnowitt, The U(1) problem: current algebra and the theta vacuum, Phys. Rev. D 23 (1981) 473 [INSPIRE].
R.D. Peccei and H.R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
J.E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].
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 [INSPIRE].
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Bolognesi, S., Konishi, K. & Luzio, A. Dynamical Abelianization and anomalies in chiral gauge theories. J. High Energ. Phys. 2022, 110 (2022). https://doi.org/10.1007/JHEP12(2022)110
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DOI: https://doi.org/10.1007/JHEP12(2022)110