Finite volume expectation values in the sine-Gordon model

TL;DR

This paper derives exact formulas for local operator expectation values in the sine-Gordon model using a fermionic basis, validating results in both UV and IR limits against known theories and semi-classical approximations.

Contribution

It introduces a novel method to compute expectation values in sine-Gordon theory using fermionic basis and confirms its accuracy through multiple limits.

Findings

Exact formulas match Liouville 3-point functions in UV limit.

Formulas agree with semi-classical predictions in IR limit.

Validation in multi-soliton sector confirms the approach's robustness.

Abstract

Using the fermionic basis discovered in the 6-vertex model, we derive exact formulas for the expectation values of local operators of the sine-Gordon theory in any eigenstate of the Hamiltonian. We tested our formulas in the pure multi-soliton sector of the theory. In the ultraviolet limit, we checked our results against Liouville 3-point functions, while in the infrared limit, we evaluated our formulas in the semi-classical limit and compared them upto 2-particle contributions against the semi-classical limit of the previously conjectured LeClair-Mussardo type formula. Complete agreement was found in both cases.