Subleading Corrections and Central Charges in the AdS/CFT Correspondence

TL;DR

The paper analyzes subleading corrections to the four-dimensional conformal anomaly coefficients $c$ and $a$ within the AdS/CFT framework, showing that $c=a$ at leading order but receiving subleading contributions in ${ m N}=1$ and ${ m N}=2$ theories from string one-loop effects. These corrections map to specific higher-derivative terms in the five-dimensional supergravity action: ${ m R}^2$ and CP-odd couplings such as $B\, ightarrow F\, ightarrow F$ (and, in some cases, $B\, ightarrow F\, ightarrow F$) that arise from ${ m R}^4$ terms in ten- or eleven-dimensional theories. The work connects these bulk corrections to the boundary current anomalies and to the quantum conformal algebra via current multiplet mixing, offering concrete field-theoretic and string-theoretic accounts for subleading $c-a$ in ${ m N}=2$ and ${ m N}=1$ theories while maintaining consistency with the absence of such corrections for ${ m N}=4$. Overall, it provides a coherent picture linking string-loop corrections, 5D supergravity couplings, and anomaly matching in the holographic context, and makes specific predictions for bulk terms such as $B\u2227 F\u2227 F$ and current-multiplet mixing effects that reflect in the boundary theory.

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.