Non-invertible defects from the Conway SCFT to K3 sigma models I: general results

Abstract

We initiate the study of supersymmetry-preserving topological defect lines (TDLs) in the Conway moonshine module $V^{f♮}$. We show that the tensor category of such defects, under suitable assumptions, admits a surjective but non-injective ring homomorphism into the ring of $\mathbb{Z}$-linear maps of the Leech lattice into itself. This puts strong constraints on possible defects and their quantum dimensions. We describe a simple construction of non-invertible TDLs from orbifolds of holomorphic (super)vertex operator algebras, which yields non-trivial examples of TDLs satisfying our main theorem. We conjecture a correspondence between four--plane--preserving TDLs in $V^{f♮}$ and supersymmetry--preserving TDLs in K3 non-linear sigma models, which extends the correspondence between symmetry groups to the level of tensor category symmetry. We establish evidence for this conjecture by constructing non-invertible TDLs in special K3 non-linear sigma models.

arXiv comment59 pages + appendices

References in corpus (34)

• Modular invariance of trace functions in orbifold theory
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Generalised twisted partition functions
• On finite symmetries and their gauging in two dimensions
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Notes on the K3 Surface and the Mathieu group M_24
• Simple currents and extensions of vertex operator algebras
• Spin TQFTs and fermionic phases of matter
• Defect lines, dualities, and generalised orbifolds
• Finite Group Modular Data
• Topological defects for the free boson CFT
• Symmetry Protected Topological phases and Generalized Cohomology
• A worldsheet extension of O(d,d;Z)
• Fermion condensation and super pivotal categories
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Holomorphic SCFTs with small index
• Fermionic CFTs and classifying algebras
• Mock Modular Mathieu Moonshine Modules
• The 290 fixed-point sublattices of the Leech lattice
• A K3 sigma model with Z_2^8:M_{20} symmetry
• The Moonshine Anomaly
• Moonshine, Superconformal Symmetry, and Quantum Error Correction
• No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons
• Parity and Spin CFT with boundaries and defects
• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• Topological defects
• Topological modularity of Supermoonshine
• Spin-cobordisms, surgeries and fermionic modular bootstrap
• Non-Invertible Symmetry in Calabi-Yau Conformal Field Theories
• BPS Algebras in 2D String Theory
• Conformal interfaces between free boson orbifold theories
• A Borcherds-Kac-Moody superalgebra with Conway symmetry
• Fun with $F_{24}$
• Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24