Subleading Corrections and Central Charges in the AdS/CFT Correspondence

TL;DR

This paper investigates subleading corrections to central charges in 4D conformal field theories within the AdS/CFT framework, analyzing their origins from string theory and implications for anomalies and effective actions.

Contribution

It identifies the string-theoretic origin of subleading corrections to central charges and anomalies in N=1 and N=2 CFTs, extending understanding of AdS/CFT correspondence.

Findings

c-a vanishes in N=4 CFT, consistent with string theory

Subleading corrections linked to R^4 terms in string effective action

Presence of specific anomaly-related terms in supergravity theories

Abstract

We explore subleading contributions to the two basic central charges c and a of four-dimensional conformal field theories in the AdS/CFT scheme. In particular we probe subleading corrections to the difference c-a from the string-theory side. In the N=4 CFT, c-a vanish identically consistently with the string-theory expectations. However, for N=1 and N=2 CFTs, the U_R(1) anomaly, which is proportional to c-a, is subleading in the large N limit for theories in the AdS/CFT context and one expects string one-loop R^2 and B \wedge R \wedge R terms in the low energy effective action. We identify these terms as coming from the R^4 terms. Similar considerations apply to the U_R(1)^3 anomaly which is, however, subleading only for N=2 theories. As a result, a string one-loop term B \wedge F \wedge F should exist in the low energy effective action of the N=4 five-dimensional supergravity. The U_R(1)^3 term is leading for the N=1 CFT and it is indeed present in the N=2 five-dimensional supergravity.