Instantons and multibananas: Relating elliptic genus and cohomological Donaldson-Thomas theory

TL;DR

This paper connects the cohomological Donaldson-Thomas invariants of local multibanana threefolds with the elliptic genus of moduli spaces of framed instanton sheaves, using hyperbolic localisation and trace formulas.

Contribution

It provides a novel computation linking Donaldson-Thomas theory and elliptic genera via hyperbolic localisation and infinite-wedge-space trace formulas.

Findings

Explicit formula for cohomological Donaldson-Thomas invariants of multibanana threefolds

Identification of these invariants with elliptic genus of framed instanton sheaves

Development of an infinite-wedge-space trace formula for elliptic genus computation

Abstract

In this article the cohomological Donaldson-Thomas theory of local multibanana threefolds is computed using Descombes' hyperbolic localisation formula. The resulting expression is precisely given by the elliptic genus of the moduli space of framed instanton sheaves. As part of the proof, an infinite-wedge-space trace formula is computed for the elliptic genus of the moduli space of framed instanton sheaves.