Deformations with Maximal Supersymmetries Part 2: Off-shell Formulation

TL;DR

This paper develops an off-shell pure spinor superspace approach to construct all-order supersymmetric deformations of maximally supersymmetric gauge theories, specifically deriving a non-Abelian Born-Infeld action.

Contribution

It introduces a method for constructing off-shell supersymmetric deformations beyond first order using pure spinor formalism, including an all-order non-Abelian Born-Infeld action.

Findings

Constructed the BV action for non-Abelian Born-Infeld deformation.

Addressed integration subtleties in pure spinor superspace.

Discussed regularization techniques relevant to the formalism.

Abstract

Continuing our exploration of maximally supersymmetric gauge theories (MSYM) deformed by higher dimensional operators, in this paper we consider an off-shell approach based on pure spinor superspace and focus on constructing supersymmetric deformations beyond the first order. In particular, we give a construction of the Batalin-Vilkovisky action of an all-order non-Abelian Born-Infeld deformation of MSYM in the non-minimal pure spinor formalism. We also discuss subtleties in the integration over the pure spinor superspace and the relevance of Berkovits-Nekrasov regularization.