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.

arXiv comment34 pages, 2 appendices, 16 figures; v2: some statements in section 4.5 corrected

References in corpus (54)

• Generalized Global Symmetries
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• TFT construction of RCFT correlators I: Partition functions
• On finite symmetries and their gauging in two dimensions
• Kramers-Wannier duality from conformal defects
• On gauging finite subgroups
• Symmetries and Strings of Adjoint QCD${}_2$
• On 2-Group Global Symmetries and Their Anomalies
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• An Invitation to Higher Gauge Theory
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Higher Algebraic Structures and Quantization
• Universal Non-Invertible Symmetries
• Cluster decomposition, T-duality, and gerby CFT's
• GLSM's for gerbes (and other toric stacks)
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• Orbifold completion of defect bicategories
• Non-birational twisted derived equivalences in abelian GLSMs
• String compactifications on Calabi-Yau stacks
• Modified instanton sum in QCD and higher-groups
• Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory
• Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Decomposition, condensation defects, and fusion
• Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics
• Sums over topological sectors and quantization of Fayet-Iliopoulos parameters
• Central Extensions of Smooth 2-Groups and a Finite-Dimensional String 2-Group
• Generalized ADE Classification of Gapped Domain Walls
• New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories
• Discrete torsion defects
• Symmetries and Anomalies of (1+1)d Theories: 2-groups and Symmetry Fractionalization
• Undoing decomposition
• Linear Sigma Models With Strongly Coupled Phases -- One Parameter Models
• Predictions for Gromov-Witten invariants of noncommutative resolutions
• Lifetimes of (near) eternal false vacua
• Decomposition in diverse dimensions
• Orbifolds and topological defects
• On gapped boundaries for SPT phases beyond group cohomology
• Anomaly resolution via decomposition
• Orbifold equivalent potentials
• Quantum symmetries in orbifolds and decomposition
• Elliptic genera of pure gauge theories in two dimensions with semisimple non-simply-connected gauge groups
• Orbifolds by 2-groups and decomposition
• D-brane probes, branched double covers, and noncommutative resolutions
• General aspects of heterotic string compactifications on stacks and gerbes
• A generalization of decomposition in orbifolds
• A Smooth Model for the String Group
• Anomalies, Extensions and Orbifolds
• Categorical Equivalence and the Renormalization Group
• On Phases of 3d $\mathcal{N}=2$ Chern-Simons-Matter Theories
• Two-dimensional gauge dynamics and the topology of singular determinantal varieties
• Decomposition in Chern-Simons theories in three dimensions
• Hybrid models for homological projective duals and noncommutative resolutions
• Landau-Ginzburg models for certain fiber products with curves

Cited by in corpus (12)

• 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
• B-brane transport in anomalous (2,2) models and localization
• Decomposition in 2d non-invertible gaugings
• Perspectives on Anomaly Resolution