A Constraint on Defect and Boundary Renormalization Group Flows

TL;DR

This paper proves that in higher-dimensional conformal field theories with defects or boundaries, a specific central charge decreases or stays constant along defect renormalization group flows, indicating a form of irreversibility.

Contribution

It establishes a monotonicity property of the defect central charge in defect RG flows using reflection positivity, extending known results to higher dimensions and boundaries.

Findings

The defect central charge b decreases or remains constant along RG flows.

The result applies to CFTs with planar defects or boundaries in dimensions d ≥ 3.

Reflection positivity is used to derive the monotonicity property.

Abstract

A conformal field theory (CFT) in dimension $d\geq 3$ coupled to a planar, two-dimensional, conformal defect is characterized in part by a "central charge" $b$ that multiplies the Euler density in the defect's Weyl anomaly. For defect renormalization group flows, under which the bulk remains critical, we use reflection positivity to show that $b$ must decrease or remain constant from ultraviolet to infrared. Our result applies also to a CFT in $d=3$ flat space with a planar boundary.