Renormalization group defects for boundary flows

TL;DR

This work extends Gaiotto’s bulk defect idea to boundary RG flows in two-dimensional CFTs by introducing boundary RG defects that encode the UV→IR operator mapping. A concrete RG pairing is defined for boundary flows via a four-point function with defect insertions, and a candidate boundary defect field is proposed for ψ_{13}-triggered flows in minimal models; explicit tests on flows such as $(2,2)\to(3,1)\oplus(1,1)$ and $(p,2)\to(p-1,1)\oplus(p+1,1)$ show that the leading UV→IR mappings reproduce known results (GRW) and that the first subleading corrections agree with conformal perturbation theory. The analysis ties the defect construction to IR g-factors, provides exact and asymptotic OPE data used to compute the pairings, and demonstrates a consistent framework for encoding boundary RG data in terms of boundary defects. These results suggest a path toward general selection rules and systematic computation of boundary flows in 2D CFTs using RG defects, with potential applications to broader classes of boundary phenomena and higher-order corrections.

Abstract

Recently Gaiotto [1] considered conformal defects which produce an expansion of infrared local fields in terms of the ultraviolet ones for a given renormalization group flow. In this paper we propose that for a boundary RG flow in two dimensions there exist boundary condition changing fields (RG defect fields) linking the UV and the IR conformal boundary conditions which carry similar information on the expansion of boundary fields at the fixed points. We propose an expression for a pairing between IR and UV operators in terms of a four-point function with two insertions of the RG defect fields. For the boundary flows in minimal models triggered by ψ_{13} perturbation we make an explicit proposal for the RG defect fields. We check our conjecture by a number of calculations done for the example of (p,2)--> (p-1,1)+(p+1,1) flows.