Anber, Mohamed M. (2021) 'Condensates and anomaly cascade in vector-like theories.', Journal of high energy physics., 2021 (3). p. 191.
We study the bilinear and higher-order fermion condensates in 4-dimensional SU(N) gauge theories with a single Dirac fermion in a general representation. Augmented with a mixed anomaly between the 0-form discrete chiral, 1-form center, and 0-form baryon number symmetries (BC anomaly), we sort out theories that admit higher-order condensates and vanishing fermion bilinears. Then, the BC anomaly is utilized to prove, in the absence of a topological quantum field theory, that nonvanishing fermion bilinears are inevitable in infrared-gapped theories with 2-index (anti)symmetric fermions. We also contrast the BC anomaly with the 0-form anomalies and show that it is the former anomaly that determines the infrared physics; we argue that the BC anomaly lurks deep to the infrared while the 0-form anomalies are just variations of local terms. We provide evidence of this assertion by studying the BC anomaly in vector-like theories compactified on a small spacial circle. These theories are weakly-coupled, under analytical control, and they admit a dual description in terms of abelian photons that determine the deep infrared dynamics. We show that the dual photons talk directly to the 1-form center symmetry in order to match the BC anomaly, while the 0-form anomalies are variations of local terms and are matched by fiat. Finally, we study the fate of the BC anomaly in the compactified theories when they are held at a finite temperature. The effective field theory that describes the low-energy physics is 2-dimensional. We show that the BC anomaly cascades from 4 to 2 dimensions.
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|Publisher Web site:||https://doi.org/10.1007/JHEP03(2021)191|
|Publisher statement:||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.|
|Date accepted:||11 February 2021|
|Date deposited:||04 October 2021|
|Date of first online publication:||09 March 2021|
|Date first made open access:||04 October 2021|
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