Non-Invertible Symmetry in Calabi-Yau Conformal Field Theories

Abstract

We construct examples of non-invertible global symmetries in two-dimensional superconformal field theories described by sigma models into Calabi-Yau target spaces. Our construction provides some of the first examples of non-invertible symmetry in irrational conformal field theories. Our approach begins at a Gepner point in the conformal manifold where the sigma model specializes to a rational conformal field theory and we can identify all supersymmetric topological Verlinde lines. By deforming away from this special locus using exactly marginal operators, we then identify submanifolds in moduli space where some non-invertible symmetry persists. For instance, along ten-dimensional loci in the complex structure moduli space of quintic Calabi-Yau threefolds there is a symmetry characterized by a Fibonacci fusion category. The symmetries we identify provide new constraints on spectra and correlation functions. As an application we show how they constrain conformal perturbation theory, consistent with recent results about scaling dimensions in the K3 sigma model near its Gepner point.

66 pages, 1 figure, Published version

References in corpus (14)

• Generalized Global Symmetries
• Duality and defects in rational conformal field theory
• Non-Invertible Duality Defects in 3+1 Dimensions
• Symmetries and Strings of Adjoint QCD${}_2$
• Orbifold groupoids
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Non-Invertible Symmetries from Holography and Branes
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Generalized Charges, Part I: Invertible Symmetries and Higher Representations
• Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases
• IIB Explored: Reflection 7-Branes

Cited by in corpus (8)

• 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
• Non-Invertible T-duality at Any Radius via Non-Compact SymTFT
• Coupling Selection Rules in Heterotic Calabi-Yau Compactifications
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models