The defect b-theorem under bulk RG flows

TL;DR

This paper investigates whether the b-theorem, which constrains defect Weyl anomaly coefficients during RG flows with fixed bulk, extends to cases where the bulk itself undergoes RG flows, finding that it does not straightforwardly apply.

Contribution

The study provides the first analysis of the b-theorem in scenarios with bulk RG flows, demonstrating its failure in perturbative examples.

Findings

The b-theorem does not hold when the bulk undergoes RG flows.

Two perturbative examples show the failure of the b-theorem extension.

The results suggest the need for revised principles in bulk and defect RG flows.

Abstract

It is known that for RG flows confined to a two-dimensional defect, where the bulk maintains its conformal nature, the coefficient of the Euler density in the defect's Weyl anomaly (termed b) cannot increase as the flow progresses from the ultraviolet to the infrared, a principle known as the b-theorem. In this paper, we investigate whether this theorem still holds when the bulk, instead of being critical, also undergoes an RG flow. To address this question, we examine two distinct and perturbatively tractable examples. Our analysis reveals that a straightforward extension of the b-theorem to these cases of RG flows fails.