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

TL;DR

This paper calculates conformal anomalies in various dimensions using higher derivative gravity in AdS/CFT, revealing new bulk theories and corrections relevant for supersymmetric and string-inspired models.

Contribution

It derives explicit conformal anomaly expressions from higher derivative gravity, expanding the AdS/CFT correspondence to include curvature squared terms and their implications.

Findings

Explicit 2D and 4D anomaly formulas with higher derivative corrections.

Higher derivative gravity theories can serve as bulk duals for certain CFTs.

Next-to-leading corrections to anomalies in supersymmetric theories are computed.

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 $L=aR^2+bR_{\mu\nu}R^{\mu\nu} + \Lambda$ (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).