Abstract
We consider the most general fractional background fluxes in the color, flavor, and baryon number directions, compatible with the faithful action of the global symmetry of a given theory. We call the obstruction to gauging symmetries revealed by such backgrounds the baryon-color-flavor (BCF) ’t Hooft anomaly. We apply the BCF anomaly to vector- like theories, with fermions in higher-dimensional representations of arbitrary N-ality, and derive non-trivial constraints on their IR dynamics. In particular, this class of theories enjoys an independent discrete chiral symmetry and one may ask about the fate of this symmetry in the background of BCF fluxes. We show that, under certain conditions, an anomaly between the chiral symmetry and the BCF background rules out massless composite fermions as the sole player in the IR: either the composites do not form or additional contributions to the matching of the BCF anomaly are required. We can also give a flavor-symmetric mass to the fermions, smaller than or of order the strong scale of the theory, and examine the θ-angle periodicity of the theory in the BCF background. Interestingly, we find that the conditions that rule out the composites are the exact same conditions that lead to an anomaly of the θ periodicity: the massive theory will experience a phase transition as we vary θ from 0 to 2π.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
D. Gaiotto, Z. Komargodski and N. Seiberg, Time-reversal breaking in QCD4 , walls and dualities in 2 + 1 dimensions, JHEP 01 (2018) 110 [arXiv:1708.06806] [INSPIRE].
M.M. Anber and E. Poppitz, Two-flavor adjoint QCD, Phys. Rev. D 98 (2018) 034026 [arXiv:1805.12290] [INSPIRE].
C. Córdova and T.T. Dumitrescu, Candidate Phases for SU(2) Adjoint QCD4 with Two Flavors from \( \mathcal{N} \) = 2 Supersymmetric Yang-Mills Theory, arXiv:1806.09592 [INSPIRE].
Z. Bi and T. Senthil, Adventure in Topological Phase Transitions in 3 + 1-D: Non-Abelian Deconfined Quantum Criticalities and a Possible Duality, Phys. Rev. X 9 (2019) 021034 [arXiv:1808.07465] [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].
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.M. Anber, Self-conjugate QCD, JHEP 10 (2019) 042 [arXiv:1906.10315] [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications I, 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, arXiv:1905.13361 [INSPIRE].
C. Choi, D. Delmastro, J. Gomis and Z. Komargodski, Dynamics of QCD3 with Rank-Two Quarks And Duality, arXiv:1810.07720 [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].
S. Bolognesi, K. Konishi and A. Luzio, Gauging 1-form center symmetries in simple SU(N) gauge theories, arXiv:1909.06598 [INSPIRE].
N. Kan, R. Kitano, S. Yankielowicz and R. Yokokura, From 3d dualities to hadron physics, arXiv:1909.04082 [INSPIRE].
A. Cherman, T. Jacobson, Y. Tanizaki and M. Ünsal, Anomalies, a mod 2 index and dynamics of 2d adjoint QCD, 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].
Y. Tanizaki and Y. Kikuchi, Vacuum structure of bifundamental gauge theories at finite topological angles, JHEP 06 (2017) 102 [arXiv:1705.01949] [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].
T. Kanazawa and M. Ünsal, Quantum distillation in QCD, arXiv:1909.05222 [INSPIRE].
G. ’t Hooft, A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories, Nucl. Phys. B 153 (1979) 141 [INSPIRE].
F. Benini, P.-S. Hsin and N. Seiberg, Comments on global symmetries, anomalies and duality in (2 + 1)d, JHEP 04 (2017) 135 [arXiv:1702.07035] [INSPIRE].
P. van Baal, Some Results for SU(N) Gauge Fields on the Hypertorus, Commun. Math. Phys. 85 (1982) 529 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1909.09027
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
Anber, M.M., Poppitz, E. On the baryon-color-flavor (BCF) anomaly in vector-like theories. J. High Energ. Phys. 2019, 63 (2019). https://doi.org/10.1007/JHEP11(2019)063
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2019)063