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

Anber, Mohamed M.; Poppitz, Erich

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


Erich Poppitz


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.


Anber, M. M., & Poppitz, E. (2019). On the baryon-color-flavor (BCF) anomaly in vector-like theories. Journal of High Energy Physics, 2019(11), Article 063.

Journal Article Type Article
Acceptance Date Oct 28, 2019
Online Publication Date Nov 11, 2019
Publication Date 2019
Deposit Date Oct 3, 2021
Publicly Available Date Oct 4, 2021
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2019
Issue 11
Article Number 063


Published Journal Article (289 Kb)

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