Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence

TL;DR

This paper investigates the conformal properties of submanifold observables in AdS/CFT, revealing invariance for odd dimensions and anomalies for even dimensions, with detailed analysis for the case of two-dimensional submanifolds.

Contribution

It provides a detailed analysis of the conformal anomaly for submanifold observables in AdS/CFT, especially focusing on the case of two-dimensional submanifolds.

Findings

Odd k submanifold observables are conformally invariant.

Even k submanifold observables exhibit a conformal anomaly.

Explicit form of the anomaly is derived for k=2.

Abstract

We analyze the conformal invariance of submanifold observables associated with $k$-branes in the AdS/CFT correspondence. For odd $k$, the resulting observables are conformally invariant, and for even $k$, they transform with a conformal anomaly that is given by a local expression which we analyze in detail for $k=2$