Computing 1/N^2 corrections in AdS/CFT

TL;DR

The paper analyzes 1/N^2 (closed-string loop) corrections in AdS/CFT by tracking CP-odd one-loop terms in IIB string theory on AdS5×SE5 and performing circle reductions to nine and five dimensions. It derives how Tr R^2 reductions on Sasaki–Einstein bases contribute to the c-a anomaly difference, obtaining concrete results: c-a=0 for S^5 and c-a=1/24 for T^{1,1}, with a general, p,q-dependent expression for Y^{p,q} spaces. The work emphasizes the necessity of circle reductions and T-duality to generate nonzero 1/N^2 shifts, and extends the analysis to lower-dimensional AdS backgrounds (AdS4 and AdS3), where analogous higher-derivative couplings arise with explicit coefficients tied to the internal geometry. Together, these results illuminate how closed-string loop effects and compactification data shape holographic Weyl anomalies and related transport/derivative corrections in AdS/CFT.

Abstract

Stringy corrections in AdS/CFT generally fall into the category of either α' effects or string loop effects, corresponding to 1/λand 1/N corrections, respectively, in the dual field theory. While α'^3R^4 corrections have been well studied, at least in the context of N=4 super-Yang-Mills, less is known about the 1/N^2 corrections arising from closed string loops. In this paper, we consider AdS_5 x SE_5 compactifications of the IIB string, and compute the closed string loop correction to the anomaly coefficients a and c in the dual field theory. For T^{1,1} reductions, we find the string loop correction to yield c-a=1/24, which is the contribution to c-a of a free N=2 hypermultiplet. We also comment on reductions to lower dimensional AdS theories as well as the nature of T-duality with higher derivatives.