Testing a novel large-Nreduction for 𝒩 = 4 super Yang-Mills theory onR×S3

Abstract

Recently a novel large-N reduction has been proposed as a maximally supersymmetric regularization of = 4 super Yang-Mills theory on R × S3 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 R × S3. At finite temperature and at weak coupling, we reproduce precisely the deconfinement phase transition in the = 4 super Yang-Mills theory on R × S3. 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 R × S3/Zq and R × S2.