Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3

TL;DR

This paper tests a new large-N reduction approach for N=4 super Yang-Mills theory on RxS^3, enabling non-perturbative studies and providing evidence for the AdS/CFT correspondence through explicit calculations of phase transitions.

Contribution

It provides a nontrivial check of the large-N reduction proposal by performing explicit calculations in the plane wave matrix model, matching known phase transitions in super Yang-Mills theory.

Findings

Reproduced the deconfinement phase transition at weak coupling.

Confirmed the phase transition corresponds to the Hawking-Page transition at strong coupling.

Extended the analysis to other curved spaces like RxS^3/Z_q and RxS^2.

Abstract

Recently a novel large-N reduction has been proposed as a maximally supersymmetric regularization of N=4 super Yang-Mills theory on RxS^3 in the planar limit. This proposal, if it works, will enable us to study the theory non-perturbatively on a computer, and hence to test the AdS/CFT correspondence analogously to the recent works on the D0-brane system. We provide a nontrivial check of this proposal by performing explicit calculations in the large-N reduced model, which is nothing but the so-called plane wave matrix model, around a particular stable vacuum corresponding to RxS^3. At finite temperature and at weak coupling, we reproduce precisely the deconfinement phase transition in the N=4 super Yang-Mills theory on RxS^3. This phase transition is considered to continue to the strongly coupled regime, where it corresponds to the Hawking-Page transition on the AdS side. We also perform calculations around other stable vacua, and reproduce the phase transition in super Yang-Mills theory on the corresponding curved space-times such as RxS^3/Z_q and RxS^2.