Topological defects in K3 sigma models

TL;DR

This paper studies topological defect lines in K3 sigma models, revealing their structure, classification, and conditions for their complexity, with implications for string theory and conformal field theory.

Contribution

It provides a classification framework for topological defects in K3 models, including conditions for their triviality or continuum nature, and tests these in specific examples.

Findings

At generic points, the defect category is trivial, generated only by the identity.

Infinite or continuum defects can occur at special points in the moduli space.

Defects have integral quantum dimension at attractor points for BPS D-brane configurations.

Abstract

We consider the topological defect lines commuting with the spectral flow and the $\mathcal{N}=(4,4)$ superconformal symmetry in two dimensional non-linear sigma models on K3. By studying their fusion with boundary states, we derive a number of general results for the category of such defects. We argue that while for certain K3 models infinitely many simple defects, and even a continuum, can occur, at generic points in the moduli space the category is actually trivial, i.e. it is generated by the identity defect. Furthermore, we show that if a K3 model is at the attractor point for some BPS configuration of D-branes, then all topological defects have integral quantum dimension. We also conjecture that a continuum of topological defects arises if and only if the K3 model is a (possibly generalized) orbifold of a torus model. Finally, we test our general results in a couple of examples, where we provide a partial classification of the topological defects.