Abstract
We study the dynamics of chiral SU(N) gauge theories. These contain Weyl fermions in the symmetric or anti-symmetric representation of the gauge group, together with further fermions in the fundamental and anti-fundamental. We revisit an old proposal of Bars and Yankielowicz who match the ‘t Hooft anomalies of this theory to free fermions. We show that there are novel and, in some cases, quite powerful constraints on the dynamics in the large N limit.
In addition, we study these SU(N) theories with an extra Weyl fermion transforming in the adjoint representation. Here we show that all 21 ‘t Hooft anomalies for global symmetries are matched with those of a Spin(8) gauge theory. This suggests a non-supersymmetric extension of the duality of Pouliot and Strassler. Finally, we also discuss some non-supersymmetric dualities with vector-like matter content for SO(N) and Sp(N) gauge theories and the constraints imposed by Weingarten inequalities.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Seiberg, Exact results on the space of vacua of four-dimensional SUSY gauge theories, Phys. Rev. D 49 (1994) 6857 [hep-th/9402044] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [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].
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].
S.R. Coleman and E. Witten, Chiral Symmetry Breakdown in Large N Chromodynamics, Phys. Rev. Lett. 45 (1980) 100.
P. Pouliot and M.J. Strassler, A Chiral SU(N) gauge theory and its nonchiral Spin(8) dual, Phys. Lett. B 370 (1996) 76 [hep-th/9510228] [INSPIRE].
O. Aharony, J. Sonnenschein, M.E. Peskin and S. Yankielowicz, Exotic nonsupersymmetric gauge dynamics from supersymmetric QCD, Phys. Rev. D 52 (1995) 6157 [hep-th/9507013] [INSPIRE].
A. Armoni, Nonsupersymmetric brane configurations, Seiberg duality, and dynamical symmetry breaking, Phys. Rev. D 89 (2014) 125025 [arXiv:1310.2027] [INSPIRE].
A. Armoni, A Note on Seiberg Duality and Chiral Symmetry Breaking, Phys. Lett. B 728 (2014) 666 [arXiv:1310.3653] [INSPIRE].
T. Appelquist, Z.-y. Duan and F. Sannino, Phases of chiral gauge theories, Phys. Rev. D 61 (2000) 125009 [hep-ph/0001043] [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].
C. Csáki, H. Murayama and O. Telem, Some exact results in chiral gauge theories, Phys. Rev. D 104 (2021) 065018 [arXiv:2104.10171] [INSPIRE].
C. Csáki, H. Murayama and O. Telem, More exact results on chiral gauge theories: The case of the symmetric tensor, Phys. Rev. D 105 (2022) 045007 [arXiv:2105.03444] [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].
A. Karasik, Anomalies for anomalous symmetries, JHEP 02 (2022) 064 [arXiv:2110.06364] [INSPIRE].
J.L. Cardy, Is There a c-Theorem in Four-Dimensions?, Phys. Lett. B 215 (1988) 749 [INSPIRE].
Z. Komargodski and A. Schwimmer, On Renormalization Group Flows in Four Dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
G. ‘t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
E. Witten, Baryons in the 1/N Expansion, Nucl. Phys. B 160 (1979) 57 [INSPIRE].
G. Veneziano, Some Aspects of a Unified Approach to Gauge, Dual and Gribov Theories, Nucl. Phys. B 117 (1976) 519 [INSPIRE].
S. Bolognesi, K. Konishi and A. Luzio, Strong anomaly and phases of chiral gauge theories, JHEP 08 (2021) 028 [arXiv:2105.03921] [INSPIRE].
J.H. Brodie, P.L. Cho and K.A. Intriligator, Misleading anomaly matchings?, Phys. Lett. B 429 (1998) 319 [hep-th/9802092] [INSPIRE].
J. Terning, ‘t Hooft anomaly matching for QCD, Phys. Rev. Lett. 80 (1998) 2517 [hep-th/9706074] [INSPIRE].
P. Pouliot and M.J. Strassler, Duality and dynamical supersymmetry breaking in Spin(10) with a spinor, Phys. Lett. B 375 (1996) 175 [hep-th/9602031] [INSPIRE].
M. Berkooz, The Dual of supersymmetric SU(2k) with an antisymmetric tensor and composite dualities, Nucl. Phys. B 452 (1995) 513 [hep-th/9505067] [INSPIRE].
P. Pouliot, Duality in SUSY SU(N) with an antisymmetric tensor, Phys. Lett. B 367 (1996) 151 [hep-th/9510148] [INSPIRE].
N. Craig, R. Essig, A. Hook and G. Torroba, New dynamics and dualities in supersymmetric chiral gauge theories, JHEP 09 (2011) 046 [arXiv:1106.5051] [INSPIRE].
N. Craig, R. Essig, A. Hook and G. Torroba, Phases of N = 1 supersymmetric chiral gauge theories, JHEP 12 (2011) 074 [arXiv:1110.5905] [INSPIRE].
I. Affleck, M. Dine and N. Seiberg, Dynamical Supersymmetry Breaking in Four-Dimensions and Its Phenomenological Implications, Nucl. Phys. B 256 (1985) 557 [INSPIRE].
E. Poppitz and S.P. Trivedi, Some examples of chiral moduli spaces and dynamical supersymmetry breaking, Phys. Lett. B 365 (1996) 125 [hep-th/9507169] [INSPIRE].
P. Pouliot, Chiral duals of nonchiral SUSY gauge theories, Phys. Lett. B 359 (1995) 108 [hep-th/9507018] [INSPIRE].
J. Preskill and S. Weinberg, “Decoupling” constraints on massless composite particles, Phys. Rev. D 24 (1981) 1059 [INSPIRE].
C. Vafa and E. Witten, Restrictions on Symmetry Breaking in Vector-Like Gauge Theories, Nucl. Phys. B 234 (1984) 173 [INSPIRE].
H.-C. Cheng and Y. Shadmi, Duality in the presence of supersymmetry breaking, Nucl. Phys. B 531 (1998) 125 [hep-th/9801146] [INSPIRE].
N. Arkani-Hamed and R. Rattazzi, Exact results for nonholomorphic masses in softly broken supersymmetric gauge theories, Phys. Lett. B 454 (1999) 290 [hep-th/9804068] [INSPIRE].
H. Murayama, Some Exact Results in QCD-like Theories, Phys. Rev. Lett. 126 (2021) 251601 [arXiv:2104.01179] [INSPIRE].
D. Weingarten, Mass Inequalities for QCD, Phys. Rev. Lett. 51 (1983) 1830 [INSPIRE].
K.A. Intriligator and N. Seiberg, Duality, monopoles, dyons, confinement and oblique confinement in supersymmetric SO(Nc) gauge theories, Nucl. Phys. B 444 (1995) 125 [hep-th/9503179] [INSPIRE].
K.A. Intriligator and P. Pouliot, Exact superpotentials, quantum vacua and duality in supersymmetric SP(Nc) gauge theories, Phys. Lett. B 353 (1995) 471 [hep-th/9505006] [INSPIRE].
E. Witten, Fermion Path Integrals And Topological Phases, Rev. Mod. Phys. 88 (2016) 035001 [arXiv:1508.04715] [INSPIRE].
L. Álvarez-Gaumé, S. Della Pietra and V. Della Pietra, The Effective Action for Chiral Fermions, Phys. Lett. B 166 (1986) 177 [INSPIRE].
E. Witten, An SU(2) Anomaly, Phys. Lett. B 117 (1982) 324 [INSPIRE].
M. Stone, Gamma matrices, Majorana fermions, and discrete symmetries in Minkowski and Euclidean signature, J. Phys. A 55 (2022) 205401 [arXiv:2009.00518] [INSPIRE].
A. Armoni, D. Israel, G. Moraitis and V. Niarchos, Non-Supersymmetric Seiberg Duality, Orientifold QCD and Non-Critical Strings, Phys. Rev. D 77 (2008) 105009 [arXiv:0801.0762] [INSPIRE].
A. Hook and G. Torroba, S-duality of nonsupersymmetric gauge theories, Phys. Rev. D 89 (2014) 025006 [arXiv:1309.5948] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2208.07842
Rights and permissions
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.
About this article
Cite this article
Karasik, A., Önder, K. & Tong, D. Chiral gauge dynamics: candidates for non-supersymmetric dualities. J. High Energ. Phys. 2022, 122 (2022). https://doi.org/10.1007/JHEP11(2022)122
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2022)122