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

Anber, Mohamed M.; Poppitz, Erich

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Erich Poppitz


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.


Anber, M. M., & Poppitz, E. (2023). Noninvertible anomalies in SU( N ) × U(1) gauge theories. Journal of High Energy Physics, 2023(8), Article 149.

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
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2023
Issue 8
Article Number 149
Keywords Anomalies in Field and String Theories, Discrete Symmetries, Global Symmetries
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