The a-theorem and conformal symmetry breaking in holographic RG flows

TL;DR

This paper investigates holographic RG flows between fixed points, focusing on conformal symmetry breaking, anomaly matching, and the properties of the dilaton mode, revealing new insights into the structure of these flows.

Contribution

It introduces a spurion field to restore Weyl invariance in holographic models and analyzes the anomalous contributions and dilaton behavior in conformal symmetry breaking flows.

Findings

Anomalous term coefficient matches conformal anomaly difference between fixed points.

Coefficient of anomaly term is positive, consistent with the holographic a-theorem.

In simple models, no dilaton pole appears in the scalar two-point function, indicating stronger singularities.

Abstract

We study holographic models describing an RG flow between two fixed points driven by a relevant scalar operator. We show how to introduce a spurion field to restore Weyl invariance and compute the anomalous contribution to the generating functional in even dimensional theories. We find that the coefficient of the anomalous term is proportional to the difference of the conformal anomalies of the UV and IR fixed points, as expected from anomaly matching arguments in field theory. For any even dimensions the coefficient is positive as implied by the holographic a-theorem. For flows corresponding to spontaneous breaking of conformal invariance, we also compute the two-point functions of the energy-momentum tensor and the scalar operator and identify the dilaton mode. Surprisingly we find that in the simplest models with just one scalar field there is no dilaton pole in the two-point function of the scalar operator but a stronger singularity. We discuss the possible implications.