Testing the AdS/CFT correspondence beyond large N

TL;DR

This paper explores testing the AdS/CFT correspondence beyond the large N limit by using the chiral SU(4)_R anomaly as a precise probe, demonstrating that 1/N^2 corrections can be matched via supergravity/string effective actions.

Contribution

It shows that the chiral anomaly provides a feasible way to test AdS/CFT beyond leading order, with exact correspondence of 1/N^2 corrections.

Findings

1/N^2 corrections to the chiral anomaly are exactly matched by supergravity/string effective action.

The chiral SU(4)_R anomaly serves as an ideal test case for beyond leading order AdS/CFT tests.

The approach extends the validity of AdS/CFT correspondence beyond the classical large N limit.

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.