A non-perturbative formulation of N=4 super Yang-Mills theory based on the large-N reduction

TL;DR

This paper investigates a non-perturbative approach to N=4 super Yang-Mills theory using large-N reduction, confirming known Wilson loop results and demonstrating a vanishing beta function at one loop.

Contribution

It provides a non-perturbative formulation of N=4 SYM via the plane wave matrix model and tests its validity through Wilson loop calculations and beta function analysis.

Findings

Wilson loop expectation value matches known results

Beta function at 1-loop vanishes in this formulation

Supports the validity of the large-N reduction approach

Abstract

We study a non-perturbative formulation of N=4 super Yang-Mills theory (SYM) on RxS^3 proposed in arXiv:0807.2352. This formulation is based on the large-N reduction, and the theory can be described as a particular large-N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S^3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.