Complex hyperk\"ahler structures defined by Donaldson-Thomas invariants

TL;DR

This paper demonstrates that Joyce structures, which encode Donaldson-Thomas invariants on CY3 categories, induce complex hyperk"ahler structures on tangent bundles, providing a geometric characterization of these metrics.

Contribution

It establishes a direct link between Joyce structures and hyperk"ahler geometry, offering a new geometric interpretation of Donaldson-Thomas invariants.

Findings

Joyce structures induce hyperk"ahler structures on tangent bundles

Hyperk"ahler metrics are characterized geometrically

Provides a new perspective on Donaldson-Thomas invariants

Abstract

The notion of a Joyce structure was introduced in arXiv:1912.06504 to describe the geometric structure on the space of stability conditions of a CY3 category naturally encoded by the Donaldson-Thomas invariants. In this paper we show that a Joyce structure on a complex manifold defines a complex hyperk\"ahler structure on the total space of its tangent bundle, and give a characterisation of the resulting hyperk\"ahler metrics in geometric terms.