Noninvertible symmetries and anomalies from gauging 1-form electric centers

Anber, Mohamed M.; Chan, Samson Y. L.

Abstract

We devise a general method for obtaining 0-form noninvertible discrete chiral symmetries in 4-dimensional SU(N)/ℤp and SU(N) × U(1)/ℤp gauge theories with matter in arbitrary representations, where ℤp is a subgroup of the electric 1-form center symmetry. Our approach involves placing the theory on a three-torus and utilizing the Hamiltonian formalism to construct noninvertible operators by introducing twists compatible with the gauging of ℤp. These theories exhibit electric 1-form and magnetic 1-form global symmetries, and their generators play a crucial role in constructing the corresponding Hilbert space. The noninvertible operators are demonstrated to project onto specific Hilbert space sectors characterized by particular magnetic fluxes. Furthermore, when subjected to twists by the electric 1-form global symmetry, these surviving sectors reveal an anomaly between the noninvertible and the 1-form symmetries. We argue that an anomaly implies that certain sectors, characterized by the eigenvalues of the electric symmetry generators, exhibit multi-fold degeneracies. When we couple these theories to axions, infrared axionic noninvertible operators inherit the ultraviolet structure of the theory, including the projective nature of the operators and their anomalies. We discuss various examples of vector and chiral gauge theories that showcase the versatility of our approach.

Citation

Anber, M. M., & Chan, S. Y. L. (2024). Noninvertible symmetries and anomalies from gauging 1-form electric centers. Journal of High Energy Physics, 2024(3), Article 169. https://doi.org/10.1007/jhep03%282024%29169

• Journal Article Type: Article
• Acceptance Date: Mar 1, 2024
• Online Publication Date: Mar 29, 2024
• Publication Date: Mar 29, 2024
• Deposit Date: May 20, 2024
• Publicly Available Date: May 20, 2024
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2024
• Issue: 3
• Article Number: 169
• DOI: https://doi.org/10.1007/jhep03%282024%29169
• Keywords: Global Symmetries, Discrete Symmetries, Anomalies in Field and String Theories
• Public URL: https://durham-repository.worktribe.com/output/2378562