Super Multi-Instantons in Conformal Chiral Superspace

TL;DR

This paper reformulates self-dual supersymmetric theories within conformal chiral superspace, making superconformal invariance explicit, and provides new multi-instanton constructions for self-dual super Yang-Mills theory.

Contribution

It introduces a new formulation of supersymmetric theories in conformal chiral superspace and extends multi-instanton constructions to this framework.

Findings

Superconformal invariance is manifest in the new superspace formulation.

Multi-instanton solutions are represented with a single constant tensor.

The approach unifies various geometric interpretations of superspace.

Abstract

We reformulate self-dual supersymmetric theories directly in conformal chiral superspace, where superconformal invariance is manifest. The superspace can be interpreted as the generalization of the usual Atiyah-Drinfel'd-Hitchin-Manin twistors (the quaternionic projective line), the real projective light-cone in six dimensions, or harmonic superspace, but can be reduced immediately to four-dimensional chiral superspace. As an example, we give the 't Hooft and ADHM multi-instanton constructions for self-dual super Yang-Mills theory. In both cases, all the parameters are represented as a single, irreducible, constant tensor.