Noninvertible anomalies in SU( N ) × U(1) gauge theories

Anber, Mohamed M.; Poppitz, Erich

Abstract

We study 4-dimensional SU(N) × U(1) gauge theories with a single massless Dirac fermion in the 2-index symmetric/antisymmetric representations and show that they are endowed with a noninvertible 0-form ℤ~2N±2χ chiral symmetry along with a 1-form ℤN1 center symmetry. By using the Hamiltonian formalism and putting the theory on a spatial three-torus T3, we construct the non-unitary gauge invariant operator corresponding to ℤ~2N±2χ and find that it acts nontrivially in sectors of the Hilbert space characterized by selected magnetic fluxes. When we subject T3 to ℤN1 twists, for N even, in selected magnetic flux sectors, the algebra of ℤ~2N±2χ and ℤN1 fails to commute by a ℤ2 phase. We interpret this noncommutativity as a mixed anomaly between the noninvertible and the 1-form symmetries. The anomaly implies that all states in the torus Hilbert space with the selected magnetic fluxes exhibit a two-fold degeneracy for arbitrary T3 size. The degenerate states are labeled by discrete electric fluxes and are characterized by nonzero expectation values of condensates. In an appendix, we also discuss how to construct the corresponding noninvertible defect via the “half-space gauging” of a discrete one-form magnetic symmetry.

Citation

Anber, M. M., & Poppitz, E. (2023). Noninvertible anomalies in SU( N ) × U(1) gauge theories. Journal of High Energy Physics, 2023(8), Article 149. https://doi.org/10.1007/jhep08%282023%29149

• Journal Article Type: Article
• Acceptance Date: Aug 15, 2023
• Online Publication Date: Aug 23, 2023
• Publication Date: 2023
• Deposit Date: Oct 16, 2023
• Publicly Available Date: Oct 16, 2023
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2023
• Issue: 8
• Article Number: 149
• DOI: https://doi.org/10.1007/jhep08%282023%29149
• Keywords: Anomalies in Field and String Theories, Discrete Symmetries, Global Symmetries
• Public URL: https://durham-repository.worktribe.com/output/1803985