A generalization of decomposition in orbifolds

Abstract

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories. However, decomposition can be, at least naively, broken in orbifolds if the orbifold has discrete torsion in the trivially-acting subgroup. (Formally, this breaks finite global one-form symmetries.) Nevertheless, even in such cases, one still sees rudiments of decomposition. In this paper, we generalize decomposition in orbifolds to include such examples of discrete torsion, which we check in numerous examples. Our analysis includes as special cases (and in one sense generalizes) quantum symmetries of abelian orbifolds.

arXiv comment71 pages, LaTeX; v2: reference added; v3: typos fixed

References in corpus (28)

• Applied Conformal Field Theory
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• On finite symmetries and their gauging in two dimensions
• On gauging finite subgroups
• Symmetries and Strings of Adjoint QCD${}_2$
• On Orbifolds with Discrete Torsion
• D-branes and Discrete Torsion II
• Cluster decomposition, T-duality, and gerby CFT's
• GLSM's for gerbes (and other toric stacks)
• String compactifications on Calabi-Yau stacks
• Non-birational twisted derived equivalences in abelian GLSMs
• Modified instanton sum in QCD and higher-groups
• Discrete Torsion
• Notes on gauging noneffective group actions
• Undoing decomposition
• Linear Sigma Models With Strongly Coupled Phases -- One Parameter Models
• Predictions for Gromov-Witten invariants of noncommutative resolutions
• Decomposition in diverse dimensions
• Elliptic genera of pure gauge theories in two dimensions with semisimple non-simply-connected gauge groups
• On Gromov-Witten theory of root gerbes
• D-brane probes, branched double covers, and noncommutative resolutions
• General aspects of heterotic string compactifications on stacks and gerbes
• Orbifolds from Modular Orbits
• GLSMs, joins, and nonperturbatively-realized geometries
• A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear sigma model
• On degree zero elliptic orbifold Gromov-Witten invariants
• Modular Orbits at Higher Genus
• On the relative dual of an $S^1$-gerbe over an orbifold

Cited by in corpus (8)

• Anomaly resolution via decomposition
• Quantum symmetries in orbifolds and decomposition
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Anomalies, Extensions and Orbifolds
• Combinatoric topological string theories and group theory algorithms
• Integrality, Duality and Finiteness in Combinatoric Topological Strings
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• Universal Deformations