Renormalization group defects for boundary flows

TL;DR

This paper introduces boundary condition changing fields, called RG defect fields, for boundary RG flows in two-dimensional models, providing a new way to understand the operator expansion at fixed points and verifying the approach with explicit calculations.

Contribution

It proposes the concept of RG defect fields linking UV and IR boundary conditions and offers an explicit expression for their pairing, supported by calculations in minimal models.

Findings

Proposed RG defect fields for boundary flows in minimal models.

Derived an expression for operator pairing via four-point functions.

Validated the conjecture through explicit calculations for specific flows.

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 \psi_{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.