Stability Conditions and Mirror Symmetry of K3 Surfaces in Attractor Backgrounds

TL;DR

This paper explores the stability conditions on K3 surfaces within mirror symmetry, especially in attractor backgrounds, revealing unique wall-crossing behaviors linked to special Lagrangians and proposing a mirror correspondence unifying homological and SYZ conjectures.

Contribution

It introduces the study of stability conditions on K3 surfaces in attractor backgrounds, highlighting non-generic wall behaviors and establishing a mirror correspondence connecting homological and SYZ mirror conjectures.

Findings

Identification of non-generic stability wall behaviors in attractor backgrounds

Mirror correspondence linking stability conditions to special Lagrangians

Synthesis of homological and SYZ mirror conjectures in this context

Abstract

We study the space of stability conditions on $K3$ surfaces from the perspective of mirror symmetry. It is done in the so called attractor backgrounds (moduli) which can be far from the conventional large complex limits and are selected by the attractor mechanism for certain black holes. We find certain highly non-generic behaviors of stability walls (a key notion in the study of wall crossings) in the space of stability conditions. They correspond via mirror symmetry to some non-generic behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of homological mirror conjecture and SYZ mirror conjecture.