On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence

TL;DR

This work extends holographic anomaly calculations to bulk gravity theories containing curvature-squared terms $\big(a R^2 + b R_{\mu\nu}R^{\mu\nu} + c R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\big)$ within the AdS/CFT framework. It develops a general holographic renormalization method and derives explicit conformal anomaly expressions in $d=2$ and $d=4$, showing how the anomalies depend on the bulk coefficients $a,b,c$ and on the AdS data $l$ and $\kappa$. The authors demonstrate that higher-derivative bulk theories can realize duals for ${\cal N}=4$ SYM in $d=4$ and, separately, for $d=2$ CFTs via three-dimensional $R^2$ gravity, including cases without the Einstein term. They further apply the formalism to compute next-to-leading corrections to the ${\cal N}=2$ SCFT trace anomaly from AdS$_5$ higher-derivative gravity, obtaining results that agree with field-theory computations (BNG) in the large-$N$ limit. Overall, the paper broadens the landscape of admissible bulk theories in AdS/CFT and provides a practical framework for incorporating stringy corrections into holographic anomalies.

Abstract

We follow to Witten proposal in the calculation of conformal anomaly from d+1-dimensional higher derivative gravity via AdS/CFT correspondence. It is assumed that some d-dimensional conformal field theories have a description in terms of above d+1-dimensional higher derivative gravity which includes not only Einstein term and cosmological constant but also curvature squared terms. The explicit expression for two-dimensional and four-dimensional anomalies is found, it contains higher derivative corrections. In particular, it is shown that not only Einstein gravity but also theory with the Lagrangian $L=aR^2+bR_{μν}R^{μν} + Λ$ (even when a=0 or b=0) is five-dimensional bulk theory for d=4 ${\cal N}=4$ super Yang-Mills theory in AdS/CFT correspondence. Similar d+1=3 theory with (or without) Einstein term may describe d=2 scalar or spinor CFTs. That gives new versions of bulk side which may be useful in different aspects. As application of our general formalism we find next-to-leading corrections to the conformal anomaly of ${\cal N}=2$ supersymmetric theory from d=5 AdS higher derivative gravity (low energy string effective action).