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Classification of compactified su(Nc) gauge theories with fermions in all representations

Anber, Mohamed M.; Vincent-Genod, Loïc

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Authors

Loïc Vincent-Genod



Abstract

We classify su(N c ) gauge theories on R3×S1 with massless fermions in higher representations obeying periodic boundary conditions along S1. In particular, we single out the class of theories that is asymptotically free and weakly coupled in the infrared, and therefore, is amenable to semi-classical treatment. Our study is conducted by carefully identifying the vacua inside the affine Weyl chamber using Verma bases and Frobenius formula techniques. Theories with fermions in pure representations are generally strongly coupled. The only exceptions are the four-index symmetric representation of su(2) and adjoint representation of su(N c ). However, we find a plethora of admissible theories with fermions in mixed representations. A sub-class of these theories have degenerate perturbative vacua separated by domain walls. In particular, su(N c ) theories with fermions in the mixed representations adjoint⊕fundamental and adjoint⊕two-index symmetric admit degenerate vacua that spontaneously break the parity P, charge conjugation C, and time reversal T symmetries. These are the first examples of strictly weakly coupled gauge theories on R3×S1 with spontaneously broken C, P, and T symmetries. We also compute the fermion zero modes in the background of monopole-instantons. The monopoles and their composites (topological molecules) proliferate in the vacuum leading to the confinement of electric charges. Interestingly enough, some theories have also accidental degenerate vacua, which are not related by any symmetry. These vacua admit different numbers of fermionic zero modes, and hence, different kinds of topological molecules. The lack of symmetry, however, indicates that such degeneracy might be lifted by higher order corrections. Finally, we study the general phase structure of adjoint⊕fundamental theories in the small circle and decompactification limits.

Citation

Anber, M. M., & Vincent-Genod, L. (2017). Classification of compactified su(Nc) gauge theories with fermions in all representations. Journal of High Energy Physics, 2017(12), Article 028. https://doi.org/10.1007/jhep12%282017%29028

Journal Article Type Article
Acceptance Date Nov 26, 2017
Online Publication Date Dec 6, 2017
Publication Date 2017
Deposit Date Oct 3, 2021
Publicly Available Date Mar 29, 2024
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2017
Issue 12
Article Number 028
DOI https://doi.org/10.1007/jhep12%282017%29028

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Copyright Statement
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.





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