# Diagonal finite volume matrix elements in the sinh-Gordon model

## TL;DR

This paper proposes exact formulas for diagonal finite volume matrix elements in the sinh-Gordon model using a fermionic basis, confirming their validity through comparisons with known three-point functions and expansions.

## Contribution

It introduces a conjecture for exact diagonal matrix elements in sinh-Gordon theory, extending previous series summations to excited states and validating them against established results.

## Key findings

- Formulas agree with Liouville three-point functions at small volumes.
- Formulas match Pozsgay's expansion at large volumes.
- Complete agreement with theoretical predictions confirms the conjecture.

## Abstract

Using the fermionic basis we conjecture exact expressions for diagonal finite volume matrix elements of exponential operators and their descendants in the sinh-Gordon theory. Our expressions sum up the LeClair-Mussardo type infinite series generalized by Pozsgay for excited state expectation values. We checked our formulae against the Liouville three-point functions for small, while against Pozsgay's expansion for large volumes and found complete agreement.