RG flows on two-dimensional spherical defects

TL;DR

This paper investigates RG flows on 2D spherical defects in conformal field theories, proposing an entropy function that decreases along the flow and equals the anomaly coefficient at fixed points, offering an alternative proof of irreversibility.

Contribution

It introduces a new entropy function for RG flows on 2D defects, demonstrating its monotonicity and relation to the anomaly coefficient, providing a novel perspective on flow irreversibility.

Findings

Entropy function decreases along RG flows.

At fixed points, entropy equals the defect's anomaly coefficient.

Explicit example illustrating the RG flow and entropy behavior.

Abstract

We study two-dimensional spherical defects in d-dimensional Conformal Field Theories. We argue that the Renormalization Group (RG) flows on such defects admit the existence of a decreasing entropy function. At the fixed points of the flow, the entropy function equals the anomaly coefficient which multiplies the Euler density in the defect's Weyl anomaly. Our construction demonstrates an alternative derivation of the irreversibility of RG flows on two-dimensional defects. Moreover in the case of perturbative RG flows, the entropy function decreases monotonically and plays the role of a C-function. We provide a simple example to explicitly work out the RG flow details in the proposed construction.