Contact Manifolds, Contact Instantons, and Twistor Geometry

TL;DR

This paper explores the twistor construction and integrability of contact instanton equations on K-contact manifolds, extending to higher dimensions and supersymmetric cases, with implications for five-dimensional supersymmetric gauge theories.

Contribution

It introduces a twistor framework for contact instantons on K-contact manifolds and discusses their integrability, extending the theory to higher dimensions and supersymmetric contexts.

Findings

Twistor construction of contact instantons on K-contact manifolds.

Analysis of integrability properties of these instantons.

Extensions to higher dimensions and supersymmetric theories.

Abstract

Recently, Kallen and Zabzine computed the partition function of a twisted supersymmetric Yang-Mills theory on the five-dimensional sphere using localisation techniques. Key to their construction is a five-dimensional generalisation of the instanton equation to which they refer as the contact instanton equation. Subject of this article is the twistor construction of this equation when formulated on K-contact manifolds and the discussion of its integrability properties. We also present certain extensions to higher dimensions and supersymmetric generalisations.