Non-invertible defects from the Conway SCFT to K3 sigma models II: duality and Fibonacci defects

TL;DR

This paper classifies and constructs topological defect lines in Conway module and K3 sigma models, revealing new duality defects, irrational quantum dimensions, and their relations to moonshine phenomena and spectral flow symmetries.

Contribution

It provides a comprehensive classification and explicit construction of non-invertible topological defect lines in Conway modules and K3 sigma models, including new examples with irrational quantum dimensions.

Findings

Classified duality defects for Tambara--Yamagami categories.

Constructed examples of TDLs with irrational quantum dimensions.

Linked TDLs in Conway modules to moonshine and spectral flow in K3 models.

Abstract

We continue the study, initiated in [hep-th:2504.18619], of topological defect lines (TDLs) in the Conway module $V^{f \natural}$ and K3 non-linear sigma models (NLSMs). In the case of $V^{f \natural}$, we fully classify the potential $N=1$ (and $N=4$)--preserving duality defects for cyclic Tambara--Yamagami categories TY$(\mathbb{Z}_N)$, 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 $V^{f \natural}$, including examples of irrational quantum dimension. In particular, we fully classify and construct defects for the TY$(\mathbb{Z}_2)$ and TY$(\mathbb{Z}_3)$ cases, and provide examples of duality defects for TY$(\mathbb{Z}_2\times \mathbb{Z}_2)$ and Fibonacci fusion categories as well. In the case of K3 NLSMs, we describe a duality defect of irrational quantum dimension $\sqrt{2}$ for the category TY$(\mathbb{Z}_2, -1)$ 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 $Rep(S_3)$ categories in particular examples. Finally we provide evidence for our conjecture in [hep-th:2504.18619] that special subcategories of such TDLs in $V^{f \natural}$ 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 $V^{f \natural}$ with coincident twining genus, and making a prediction for a number of TDLs in K3 NLSMs yet to be found.