2025/12/22 by Roberta Angius, Angius, Roberta, Stefano Giaccari +5
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2512.19640
openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
We continue the study, initiated in [hep-th:2504.18619], of topological defect lines (TDLs) in the Conway module Vf \natural and K3 non-linear sigma models (NLSMs). In the case of Vf \natural, we fully classify the potential N=1 (and N=4)--preserving duality defects for cyclic Tambara--Yamagami categories TY(ℤN), noting a curious relation to genus zero groups of monstrous moonshine. We use the correspondence with Leech lattice endomorphisms, discovered in [hep-th:2504.18619], to construct a number of non-trivial examples of TDLs in Vf \natural, including examples of irrational quantum dimension. In particular, we fully classify and construct defects for the TY(ℤ2) and TY(ℤ3) cases, and provide examples of duality defects for TY(ℤ2× ℤ2) and Fibonacci fusion categories as well. In the case of K3 NLSMs, we describe a duality defect of irrational quantum dimension √(2) for the category TY(ℤ2, -1) in a particular torus orbifold, which exists on a 16-dimensional slice of the moduli space. We also provide a detailed analysis of spectral flow--preserving TDLs in Gepner models of K3, of independent interest, and use this to construct non-invertible defects for Fibonacci and Rep(S3) categories in particular examples. Finally we provide evidence for our conjecture in [hep-th:2504.18619] that special subcategories of such TDLs in Vf \natural correspond to N=(4,4) and spectral flow--preserving defect lines in a corresponding K3 NLSM. In particular, we compute defect--twined elliptic genera for all non-invertible defects constructed in this article, demonstrating that for each defect found in a K3 NLSM, there is a corresponding defect in Vf \natural with coincident twining genus, and making a prediction for a number of TDLs in K3 NLSMs yet to be found.