Super Yang-Mills Theory as a Random Matrix Model

TL;DR

This paper connects super Yang-Mills theory to a random matrix model, revealing cancellations and universal limits that could model gravitational strings with self-duality.

Contribution

It generalizes the Gervais-Neveu gauge to four-dimensional N=1 superspace, linking super Yang-Mills theory to a superstring theory on a random lattice.

Findings

All chiral superfields cancel to all loops.

The remaining scalar superfield has a renormalizable massive propagator.

Finite matrix models have a universal large-color limit.

Abstract

We generalize the Gervais-Neveu gauge to four-dimensional N=1 superspace. The model describes an N=2 super Yang-Mills theory. All chiral superfields (N=2 matter and ghost multiplets) exactly cancel to all loops. The remaining hermitian scalar superfield (matrix) has a renormalizable massive propagator and simplified vertices. These properties are associated with N=1 supergraphs describing a superstring theory on a random lattice world-sheet. We also consider all possible finite matrix models, and find they have a universal large-color limit. These could describe gravitational strings if the matrix-model coupling is fixed to unity, for exact electric-magnetic self-duality.