Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds

Abstract

String / M-theory backgrounds with degrees of freedom at a localized singularity provide a general template for generating strongly correlated systems decoupled from lower-dimensional gravity. There are by now several complementary procedures for extracting the associated generalized symmetry data from orbifolds of the form ${\mathbb{R}}^6/\Gamma$, including methods based on the boundary topology of the asymptotic geometry, as well as the adjacency matrix for fermionic degrees of freedom in the quiver gauge theory of probe branes. In this paper we show that this match between the two methods also works in non-supersymmetric and discrete torsion backgrounds. In particular, a refinement of geometric boundary data based on Chen-Ruan cohomology matches the expected answer based on quiver data. Additionally, we also show that free (i.e., non-torsion) factors count the number of higher-dimensional branes which couple to the localized singularity. We use this to also extract quadratic pairing terms in the associated symmetry theory (SymTh) for these systems, and explain how these considerations generalize to a broader class of backgrounds.

57 pages + appendices, 12 figures

References in corpus (47)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Non-Invertible Symmetries from Holography and Branes
• The Branes Behind Generalized Symmetry Operators
• Branes and Non-Invertible Symmetries
• Turaev-Viro invariants as an extended TQFT
• 2-Group Symmetries and M-Theory
• Higher Symmetries of 5d Orbifold SCFTs
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• Anomalies and gauging of U(1) symmetries
• 5D and 6D SCFTs from ${\mathbb{C}}^3$ orbifolds
• On the Holographic Dual of a Topological Symmetry Operator
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases
• On the Symmetry TFT of Yang-Mills-Chern-Simons theory
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Quantum symmetries in orbifolds and decomposition
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Orbifolds by 2-groups and decomposition
• Symmetry TFTs for Non-Invertible Defects
• Notes on gauging noninvertible symmetries, part 2: higher multiplicity cases
• Matching higher symmetries across Intriligator-Seiberg duality
• A SymTFT for Continuous Symmetries
• Top Down Approach to Topological Duality Defects
• Cornering Relative Symmetry Theories
• Fluxbranes, Generalized Symmetries, and Verlinde's Metastable Monopole
• Non-invertible Symmetries in 2D from Type IIB String Theory
• The Crepant Resolution Conjecture
• R7-Branes as Charge Conjugation Operators
• Aspects of Categorical Symmetries from Branes: SymTFTs and Generalized Charges
• SymTrees and Multi-Sector QFTs
• Junctions, Edge Modes, and $G_2$-Holonomy Orbifolds
• Metric Isometries, Holography, and Continuous Symmetry Operators
• Global Structures from the Infrared
• Anomaly resolution by non-invertible symmetries
• Gauging in Parameter Space: A Top-Down Perspective
• Generalized Symmetries in 2D from String Theory: SymTFTs, Intrinsic Relativeness, and Anomalies of Non-invertible Symmetries
• Generalized Symmetries, Gravity, and the Swampland
• On the Holographic Dual of a Symmetry Operator at Finite Temperature
• Generalized Symmetries of Non-Supersymmetric Orbifolds
• Symmetries Beyond Branes: Geometric Engineering and Isometries
• Celestial Topology, Symmetry Theories, and Evidence for a Non-SUSY D3-Brane CFT
• Some aspects of symmetry descent
• Non-Invertible Symmetries in 6d from Green-Schwarz Automorphisms
• SymTFTs for $U(1)$ symmetries from descent
• SymTFTs and Non-Invertible Symmetries of 6d (2,0) SCFTs of Type $D$ from M-theory
• Consequences of Symmetry Fractionalization without 1-Form Global Symmetries