Boundary and Interface CFTs from the Conformal Bootstrap

TL;DR

This paper applies the conformal bootstrap to defect conformal field theories, analyzing boundary and interface effects in 3d and 4-epsilon dimensions, providing numerical estimates of spectra and OPE coefficients.

Contribution

It introduces a numerical bootstrap approach to defect CFTs, deriving bulk and surface operator spectra and OPE coefficients, and extends analysis to RG interfaces in 4-epsilon dimensions.

Findings

Bulk spectrum information obtained from surface data in the extraordinary transition.

Calculated the scale dimension of surface operators in the ordinary transition, matching two-loop results.

Numerical estimates of OPE coefficients and analysis of RG interfaces in 4-epsilon dimensions.

Abstract

We explore some consequences of the crossing symmetry for defect conformal field theories, focusing on codimension one defects like flat boundaries or interfaces. We study surface transitions of the 3d Ising and other O(N) models through numerical solutions to the crossing equations with the method of determinants. In the extraordinary transition, where the low-lying spectrum of the surface operators is known, we use the bootstrap equations to obtain information on the bulk spectrum of the theory. In the ordinary transition the knowledge of the low-lying bulk spectrum allows to calculate the scale dimension of the relevant surface operator, which compares well with known results of two-loop calculations in 3d. Estimates of various OPE coefficients are also obtained. We also analyze in 4-epsilon dimensions the renormalization group interface between the O(N) model and the free theory and check numerically the results in 3d.