Conformal Anomaly for Dilaton Coupled Theories from AdS/CFT Correspondence

TL;DR

This paper derives the conformal anomaly for dilaton-coupled theories on curved backgrounds using AdS/CFT correspondence, providing new insights into anomalies in various dimensions and simplifying calculations compared to traditional QFT methods.

Contribution

It introduces a supergravity-based method to compute dilaton-dependent conformal anomalies across different dimensions, enhancing understanding of anomalies in string theory and holography.

Findings

Conformal anomaly for dilaton coupled theories derived from supergravity.

Agreement with known 2D anomalies up to total derivative terms.

Simplified calculation method for higher-dimensional anomalies.

Abstract

Trace anomaly for dilaton coupled conformal theories on curved background with non-zero dilaton is found from supergravity side as an IR effect using AdS/CFT correspondence. For $d=2$ it coincides with the conformal anomaly for dilaton coupled scalar (up to total derivative term which is known to be ambiguous). In four-dimensional case we get conformal anomaly for ${\cal N}=4$ super YM theory interacting with conformal supergravity. In the same way the calculation of dilaton dependent conformal anomaly in higher dimensions seems to be much easier than using standard QFT methods.