A Constraint on Defect and Boundary Renormalization Group Flows

TL;DR

For defect renormalization group flows, under which the bulk remains critical, reflection positivity is used to show that b must decrease or remain constant from the ultraviolet to the infrared.

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.