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

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.