Journal of High Energy Physics

, 2019:63 | Cite as

On the baryon-color-flavor (BCF) anomaly in vector-like theories

  • Mohamed M. AnberEmail author
  • Erich Poppitz
Open Access
Regular Article - Theoretical Physics


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.


Anomalies in Field and String Theories Discrete Symmetries Global Symmetries 


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


  1. [1]
    D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP02 (2015) 172 [arXiv:1412.5148] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, Theta, Time Reversal and Temperature, JHEP05 (2017) 091 [arXiv:1703.00501] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    D. Gaiotto, Z. Komargodski and N. Seiberg, Time-reversal breaking in QCD4 , walls and dualities in 2 + 1 dimensions, JHEP01 (2018) 110 [arXiv:1708.06806] [INSPIRE].
  4. [4]
    M.M. Anber and E. Poppitz, Two-flavor adjoint QCD, Phys. Rev.D 98 (2018) 034026 [arXiv:1805.12290] [INSPIRE].
  5. [5]
    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].
  6. [6]
    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].
  7. [7]
    Z. Wan and J. Wang, Adjoint QCD 4, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory and Higher Symmetry-Extension, Phys. Rev.D 99 (2019) 065013 [arXiv:1812.11955] [INSPIRE].
  8. [8]
    M.M. Anber and E. Poppitz, Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj), JHEP05 (2019) 151 [arXiv:1811.10642] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    M.M. Anber, Self-conjugate QCD, JHEP10 (2019) 042 [arXiv:1906.10315] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    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].
  11. [11]
    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].
  12. [12]
    C. Choi, D. Delmastro, J. Gomis and Z. Komargodski, Dynamics of QCD 3with Rank-Two Quarks And Duality, arXiv:1810.07720 [INSPIRE].
  13. [13]
    M.M. Anber and E. Poppitz, Anomaly matching, (axial) Schwinger models and high-T super Yang-Mills domain walls, JHEP09 (2018) 076 [arXiv:1807.00093] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    S. Bolognesi, K. Konishi and A. Luzio, Gauging 1-form center symmetries in simple SU(N) gauge theories, arXiv:1909.06598 [INSPIRE].
  15. [15]
    N. Kan, R. Kitano, S. Yankielowicz and R. Yokokura, From 3d dualities to hadron physics, arXiv:1909.04082 [INSPIRE].
  16. [16]
    A. Cherman, T. Jacobson, Y. Tanizaki and M. Ünsal, Anomalies, a mod 2 index and dynamics of 2d adjoint QCD, arXiv:1908.09858 [INSPIRE].
  17. [17]
    H. Shimizu and K. Yonekura, Anomaly constraints on deconfinement and chiral phase transition, Phys. Rev.D 97 (2018) 105011 [arXiv:1706.06104] [INSPIRE].ADSGoogle Scholar
  18. [18]
    Y. Tanizaki and Y. Kikuchi, Vacuum structure of bifundamental gauge theories at finite topological angles, JHEP06 (2017) 102 [arXiv:1705.01949] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    Y. Tanizaki, Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking, JHEP08 (2018) 171 [arXiv:1807.07666] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    T. Kanazawa and M. Ünsal, Quantum distillation in QCD, arXiv:1909.05222 [INSPIRE].
  21. [21]
    G. ’t Hooft, A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories, Nucl. Phys.B 153 (1979) 141 [INSPIRE].
  22. [22]
    F. Benini, P.-S. Hsin and N. Seiberg, Comments on global symmetries, anomalies and duality in (2 + 1)d, JHEP04 (2017) 135 [arXiv:1702.07035] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    P. van Baal, Some Results for SU(N) Gauge Fields on the Hypertorus, Commun. Math. Phys.85 (1982) 529 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsLewis & Clark CollegePortlandU.S.A.
  2. 2.Department of PhysicsUniversity of TorontoTorontoCanada

Personalised recommendations