Form factor relocalisation and interpolating renormalisation group flows from the staircase model

TL;DR

This paper explores the staircase model in two-dimensional conformal field theory, revealing a relocalisation mechanism in spectral integrals that offers new insights into form factors and RG flows.

Contribution

It introduces a novel relocalisation phenomenon in spectral integrals for integrable RG flows, enhancing the construction of form factors in non-diagonal scattering models.

Findings

The c-function matches Zamolodchikov's TBA results.

Spectral integrals exhibit a localisation pattern due to relocalisation.

Proposes a new approach for form factor construction in integrable models.

Abstract

We investigate the staircase model, introduced by Aliosha Zamolodchikov through an analytic continuation of the sinh-Gordon S-matrix to describe interpolating flows between minimal models of conformal field theory in two dimensions. Applying the form factor expansion and the c-theorem, we show that the resulting c-function has the same physical content as that found by Zamolodchikov from the thermodynamic Bethe Ansatz. This turns out to be a consequence of a nontrivial underlying mechanism, which leads to an interesting localisation pattern for the spectral integrals giving the multi-particle contributions. We demonstrate several aspects of this form factor relocalisation, which suggests a novel approach to the construction of form factors and spectral sums in integrable renormalisation group flows with non-diagonal scattering.