Irrelevant Operators and their Holographic Anomalies

TL;DR

This paper explores how irrelevant operators in a conformal field theory influence Weyl anomalies through holographic methods, analyzing the backreaction of a massive scalar field on the bulk metric within the AdS/CFT framework.

Contribution

It provides a holographic description of boundary metric beta-functions and anomalies induced by irrelevant operators, considering backreaction effects in the bulk.

Findings

Holographic relation between bulk diffeomorphisms and boundary Weyl transformations.

Modification of Weyl anomalies due to irrelevant operators.

Validation of AdS/CFT correspondence through backreaction analysis.

Abstract

Irrelevant operators in a CFT modify the usual Weyl transformation of the metric. A metric beta-function turns on, which modifies the Weyl anomalies as well. In this paper, we study the relation between bulk diffeomorphisms and Weyl transformation at the boundary when a massive scalar field, which sources irrelevant operators at the boundary, is coupled to the bulk metric. Considering the effect of the backreaction generated by the scalar field, we provide a holographic description of the boundary metric beta-function and anomalies. Our results represent an additional test of the AdS/CFT correspondence.