Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory

TL;DR

This paper explores methods to incorporate mass terms into three-dimensional twistor string theory, connecting it to super Yang-Mills theory with massive particles and analyzing their higher-dimensional counterparts.

Contribution

It adapts twistor string models to 3D super Yang-Mills, constructs topological string theories with massive fields, and extends some results to 4D with superconformal gravity insights.

Findings

Constructed B-model topological strings for massive 3D super Yang-Mills.

Identified enhanced R-symmetry in Berkovits's model.

Extended some constructions to 4D with superconformal gravity.

Abstract

We propose various ways of adding mass terms to three-dimensional twistor string theory. We begin with a review of mini-twistor space--the reduction of D=4 twistor space to D=3. We adapt the two proposals for twistor string theory, Witten's and Berkovits's, to D=3 super Yang-Mills theory. In Berkovits's model, we identify the enhanced R-symmetry. We then construct B-model topological string theories that, we propose, correspond to D=3 Yang-Mills theory with massive spinors and massive and massless scalars in the adjoint representation of the gauge group. We also analyze the counterparts of these constructions in Berkovits's model. Some of our constructions can be lifted to D=4, where infinitesimal mass terms correspond to VEVs of certain superconformal gravity fields.