Testing the AdS/CFT correspondence beyond large N

Abstract

According to the AdS/CFT correspondence, the maximally supersymmetric SU(N) Yang-Mills theory in 4 dimensions is dual to the type IIB string theory compactified on AdS_5 x S^5. Most of the tests performed so far are confined to the leading order at large N or equivalently string tree-level. To probe the correspondence beyond this leading order and obtain 1/N^2 corrections is difficult since string one-loop computations on an AdS_5 x S^5 background generally are beyond feasibility. However, we will show that the chiral SU(4)_R anomaly of the super YM theory provides an ideal testing ground to go beyond leading order in N. We review and develop further our previous results that the 1/N^2 corrections to the chiral anomaly on the super YM side can be exactly accounted for by the supergravity/string effective action induced at one loop.