Supersymmetric Yang-Mills Theory and Riemannian Geometry

TL;DR

This paper develops a geometric framework for N=1 supersymmetric Yang-Mills theory by introducing gauge-invariant variables that reveal an underlying supergravity geometry, avoiding divergences present in non-supersymmetric cases.

Contribution

It constructs a geometrical interpretation of supersymmetric Yang-Mills theory using gauge-invariant variables, linking it to supergravity geometry and resolving divergence issues.

Findings

Gauge-invariant variables parameterize the physical Hilbert space.

Emergent geometry corresponds to N=1 supergravity with torsion.

Divergences from differential operator inversion are absent in supersymmetric case.

Abstract

We introduce new local gauge invariant variables for N=1 supersymmetric Yang-Mills theory, explicitly parameterizing the physical Hilbert space of the theory. We show that these gauge invariant variables have a geometrical interpretation, and can be constructed such that the emergent geometry is that of N=1 supergravity: a Riemannian geometry with vector-spinor generated torsion. Full geometrization of supersymmetric Yang-Mills theory is carried out, and geometry independent divergences associated to the inversion of a differential operator with zero modes -- that were encountered in the non-supersymmetric case -- do not arise in this situation.