Renormalization Group Flows on Line Defects

TL;DR

This paper extends the concept of the g theorem to line defects in conformal field theories, demonstrating that RG flows on such defects are irreversible and possess a decreasing entropy function, with applications to Wilson loops in 4D.

Contribution

It introduces a generalized g theorem for line defects in arbitrary dimensions, establishing irreversibility and a canonical entropy function for RG flows on these defects.

Findings

RG flows on line defects are irreversible.

A canonical decreasing entropy function exists for these flows.

Application to Wilson loops in 4D confirms the theoretical framework.

Abstract

We consider line defects in d-dimensional Conformal Field Theories (CFTs). The ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. We show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. We demonstrate our results in a flow between Wilson loops in 4 dimensions.