Sine-Gordon form factors in finite volume

TL;DR

This paper compares sine-Gordon form factors obtained via bootstrap to finite volume matrix elements from the truncated conformal space approach, addressing soliton effects and exponential corrections to validate the formalism.

Contribution

It extends the formalism for finite volume matrix elements to include solitons and mu-term corrections, providing a comprehensive comparison with numerical data.

Findings

High success in matching most matrix elements

Identification of discrepancies in some breather matrix elements with disconnected pieces

Discussion on mu-term effects influencing operator matrix element extraction

Abstract

We compare form factors in sine-Gordon theory, obtained via the bootstrap, to finite volume matrix elements computed using the truncated conformal space approach. For breather form factors, this is essentially a straightforward application of a previously developed formalism that describes the volume dependence of operator matrix elements up to corrections exponentially decaying with the volume. In the case of solitons, it is necessary to generalize the formalism to include effects of non-diagonal scattering. In some cases it is also necessary to take into account some of the exponential corrections (so-called mu-terms) to get agreement with the numerical data. For almost all matrix elements the comparison is a success, with the puzzling exception of some breather matrix elements that contain disconnected pieces. We also give a short discussion of the implications of the observed behaviour of mu-terms on the determination of operator matrix elements from finite volume data, as occurs e.g. in the context of lattice field theory.