Decomposition, Trivially-Acting Symmetries, and Topological Operators

Abstract

Trivially-acting symmetries in two-dimensional conformal field theory include twist fields of dimension zero which are local topological operators. We investigate the consequences of regarding these operators as part of the global symmetry of the theory. That is, we regard such a symmetry as a mix of topological defect lines (TDLs) and topological point operators (TPOs). TDLs related by a trivially-acting symmetry can join at a TPO to form non-trivial two-way junctions. Upon gauging, the local operators at those junctions can become vacua in a disjoint union of theories. Examining the behavior of the TPOs under gauging therefore allows us to refine decomposition by tracking the trivially-acting symmetries of each universe. Mixed anomalies between the TDLs and TPOs provide discrete torsion-like phases for the partition functions of these orbifolds, modifying the resulting decomposition. This framework also readily allows for the consideration of trivially-acting non-invertible symmetries.

34 pages, 2 appendices, 16 figures; v2: some statements in section 4.5 corrected

References in corpus (10)

• Generalized Global Symmetries
• Universal Non-Invertible Symmetries
• Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
• Decomposition, condensation defects, and fusion
• Discrete torsion defects
• Undoing decomposition
• Decomposition in diverse dimensions
• Orbifolds by 2-groups and decomposition
• Anomalies, Extensions and Orbifolds
• Decomposition in Chern-Simons theories in three dimensions

Cited by in corpus (11)

• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Decomposition and the Gross-Taylor string theory
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• Decomposition squared
• Non-Invertible Gauss Law and Axions
• Anomaly resolution by non-invertible symmetries
• Decomposition in 2d non-invertible gaugings
• Perspectives on Anomaly Resolution