N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature

TL;DR

This paper demonstrates that the plane wave matrix model effectively reproduces the thermodynamic properties of N=4 supersymmetric Yang-Mills theory on S^3 at high temperature, providing a nonperturbative approach for analysis.

Contribution

It derives the N=4 SYM action on R×S^3 from the plane wave matrix model and evaluates its effective action at finite temperature, confirming the model's validity for nonperturbative studies.

Findings

Effective action matches the free energy of N=4 SYM at high temperature

Plane wave matrix model reproduces key thermodynamic features

Supports using the model for nonperturbative analysis

Abstract

We investigate the large N reduced model of gauge theory on a curved spacetime through the plane wave matrix model. We formally derive the action of the N=4 supersymmetric Yang-Mills theory on R \times S^3 from the plane wave matrix model in the large N limit. Furthermore, we evaluate the effective action of the plane wave matrix model up to the two-loop level at finite temperature. We find that the effective action is consistent with the free energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature limit where the planar contributions dominate. We conclude that the plane wave matrix model can be used as a large N reduced model to investigate nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \times S^3.