Direct test of the AdS/CFT correspondence by Monte Carlo studies of $ \mathcal{N}=4 $ super Yang-Mills theory

Abstract

We perform nonperturbative studies of N=4 super Yang-Mills theory by Monte Carlo simulation. In particular, we calculate the correlation functions of chiral primary operators to test the AdS/CFT correspondence. Our results agree with the predictions obtained from the AdS side that the SUSY non-renormalization property is obeyed by the three-point functions but \emph{not} by the four-point functions investigated in this paper. Instead of the lattice regularization, we use a novel regularization of the theory based on an equivalence in the large-N limit between the N=4 SU(N) theory on RxS^3 and a one-dimensional SU(N) gauge theory known as the plane-wave (BMN) matrix model. The equivalence extends the idea of large-N reduction to a curved space and, at the same time, overcomes the obstacle related to the center symmetry breaking. The adopted regularization preserves 16 SUSY, which is crucial in testing the AdS/CFT correspondence with the available computer resources. The only SUSY breaking effects, which come from the momentum cutoff $\Lambda$ in R direction, are made negligible by using sufficiently large $\Lambda$.