One-point functions in perturbed boundary conformal field theories

TL;DR

This work analyzes bulk and boundary one-point functions in the boundary scaling Lee-Yang model, employing both form-factor expansions and truncated conformal space (TCSA) techniques to achieve cross-method validation. A key finding is that a modest correction to the Ghoshal–Zamolodchikov boundary state (effectively a factor of 2 in the odd-particle sector) is required for consistency between FF and TCSA results. The study also derives exact finite-width expressions for boundary observables via TBA in both L-channel and R-channel pictures, and uncovers an off-critical identity relating cylinder partition functions with different boundary conditions, with implications for boundary RG flows and vacuum stability on finite strips. Overall, the results establish strong concordance among FF, TCSA, and TBA approaches and illuminate how boundary perturbations influence spectra, flows, and stability in non-unitary boundary CFTs, suggesting pathways to extend these methods to more complex models.

Abstract

We consider the one-point functions of bulk and boundary fields in the scaling Lee-Yang model for various combinations of bulk and boundary perturbations. The one-point functions of the bulk fields are analysed using the truncated conformal space approach and the form-factor expansion. Good agreement is found between the results of the two methods, though we find that the expression for the general boundary state given by Ghoshal and Zamolodchikov has to be corrected slightly. For the boundary fields we use thermodynamic Bethe ansatz equations to find exact expressions for the strip and semi-infinite cylinder geometries. We also find a novel off-critical identity between the cylinder partition functions of models with differing boundary conditions, and use this to investigate the regions of boundary-induced instability exhibited by the model on a finite strip.