Holomorphic Superspace

TL;DR

This paper develops a twisted holomorphic superspace framework for N=1 super-Yang-Mills theory in four dimensions, providing new methods to solve constraints and exploring connections to higher-dimensional theories.

Contribution

It introduces a novel holomorphic superspace description for N=1 super-Yang-Mills, including solutions with and without a prepotential, and relates N=1 and N=2 holomorphic superspaces.

Findings

Provides a twisted holomorphic superspace formulation for N=1 super-Yang-Mills.

Solves the superspace constraints using two different approaches.

Suggests potential applications to N=1, d=10 super-Yang-Mills theory.

Abstract

We give a twisted holomorphic superspace description for the super-Yang-Mills theory, using holomorphic and antiholomorphic decompositions of twisted spinors. We consider the case of the N=1 super-Yang-Mills theory in four dimensions. We solve the constraints in two different manners, without and with a prepotential. This might have further application for an holomorphic superspace description of N=1,d=10 theory. We also explain how the N=1 and N=2 holomorphic superspaces are related.