On Hidden Symmetries of a Super Gauge Theory and Twistor String Theory

TL;DR

This paper uncovers infinite-dimensional hidden symmetries in N-extended self-dual super Yang-Mills equations using supertwistor methods, linking them to integrable models and topological string theories.

Contribution

It introduces the construction of super Yang-Mills hierarchies via supertwistor space and relates these hierarchies to topological B-models and integrable systems.

Findings

Identified infinite-dimensional hidden symmetry algebras.

Constructed super Yang-Mills hierarchies from supertwistor space.

Connected hierarchies to topological string theories and integrable models.

Abstract

We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the N-extented self-dual super Yang-Mills equations for general N\leq4 by using the supertwistor correspondence. Furthermore, by enhancing the supertwistor space, we construct the N-extended self-dual super Yang-Mills hierarchies, which describe infinite sets of graded Abelian symmetries. We also show that the open topological B-model with the enhanced supertwistor space as target manifold will describe the hierarchies. Furthermore, these hierarchies will in turn -- by a supersymmetric extension of Ward's conjecture -- reduce to the super hierarchies of integrable models in D<4 dimensions.