Holographic Trace Anomaly and Local Renormalization Group

TL;DR

This paper uses the Hamilton-Jacobi method in holography to compute trace anomalies in 4D and 6D CFTs, linking holographic and local RG, and exploring effects of scalar fields and higher-derivative gravity.

Contribution

It extends the Hamilton-Jacobi approach to include higher-derivative gravity and scalar interactions, establishing a holographic derivation of the local RG equation and its consistency conditions.

Findings

Computed holographic trace anomalies for 4D and 6D CFTs.

Established the holographic derivation of the local RG equation.

Analyzed effects of scalar fields on the anomaly and RG flow.

Abstract

The Hamilton-Jacobi method in holography has produced important results both at a renormalization group (RG) fixed point and away from it. In this paper we use the Hamilton-Jacobi method to compute the holographic trace anomaly for four- and six-dimensional boundary conformal field theories (CFTs), assuming higher-derivative gravity and interactions of scalar fields in the bulk. The scalar field contributions to the anomaly appear in CFTs with exactly marginal operators. Moving away from the fixed point, we show that the Hamilton-Jacobi formalism provides a deep connection between the holographic and the local RG. We derive the local RG equation holographically, and verify explicitly that it satisfies Weyl consistency conditions stemming from the commutativity of Weyl scalings. We also consider massive scalar fields in the bulk corresponding to boundary relevant operators, and comment on their effects to the local RG equation.