# Nonperturbative functional renormalization-group approach to the sine-Gordon model and the Lukyanov-Zamolodchikov conjecture

## TL;DR

This paper applies a nonperturbative functional renormalization-group method to the sine-Gordon model, benchmarking results against exact solutions and testing the Lukyanov-Zamolodchikov conjecture for exponential field expectation values.

## Contribution

It introduces a nonperturbative FRG approach to the sine-Gordon model and validates the Lukyanov-Zamolodchikov conjecture with high precision.

## Key findings

- FRG results agree with exact soliton and breather masses
- Discrepancies in the conjecture are less than 1%
- Method provides accurate nonperturbative insights into the model

## Abstract

We study the quantum sine-Gordon model within a nonperturbative functional renormalization-group approach (FRG). This approach is benchmarked by comparing our findings for the soliton and lightest breather (soliton-antisoliton bound state) masses to exact results. We then examine the validity of the Lukyanov-Zamolodchikov conjecture for the expectation value $\langle e^{\frac{i}{2}n\beta\varphi}\rangle$ of the exponential fields in the massive phase ($n$ is integer and $2\pi/\beta$ denotes the periodicity of the potential in the sine-Gordon model). We find that the minimum of the relative and absolute disagreements between the FRG results and the conjecture is smaller than 0.01.