On Subleading Contributions to the AdS/CFT Trace Anomaly

TL;DR

The authors compute subleading (order N) contributions to the 4D trace anomaly in the AdS/CFT context by identifying bulk ${R^{2}}$ and ${F^{2}}$ terms via heterotic-type I duality and tracking their impact on the holographic conformal anomaly. They demonstrate that the ${R^{2}}$ term reproduces the $(a-c)$-dependent part of the subleading anomaly and that the external flavor ${F^{2}}$ contribution matches the corresponding field-theory term, while noting a remaining volume-like piece likely tied to undetermined ${ m AdS}_{5}$ cosmological constant or other higher-derivative terms. The analysis is extended to ${ m SO}$ and ${ m Sp}$ ${ m N}=4$ theories, where orientifold-induced RR charge shifts explain the linear in N corrections, consistent with expectations. The results corroborate the AdS/CFT correspondence at subleading order for anomalies but also highlight gaps in our understanding of ${ m abla}^4$-level bulk terms and RR backgrounds. Overall, the paper shows that subleading anomalies can be encoded in higher-derivative bulk actions, while fully fixing them requires a more complete string-theoretic treatment of RR sectors.

Abstract

In the context of the AdS/CFT correspondence, we perform a direct computation in AdS_5 supergravity of the trace anomaly of a d=4, N=2 SCFT. We find agreement with the field theory result up to next to leading order in the 1/N expansion. In particular, the order N gravitational contribution to the anomaly is obtained from a Riemann tensor squared term in the 7-brane effective action deduced from heterotic - type I duality. We also discuss, in the AdS/CFT context, the order N corrections to the trace anomaly in d=4, N=4 SCFTs involving SO or Sp gauge groups.