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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

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.

Keywords

Anomalies in Field and String Theories Discrete Symmetries Global Symmetries 

Notes

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

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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

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