PreprintCC BY 4.0arXiv
Probabilistic ultraviolet renormalization of the two-dimensional Sine-Gordon model
Abstract
We give a probabilistic approach to the ultraviolet renormalization of the two-dimensional Sine-Gordon model. The model is formally described by the density exp(α∫ mathopen: cos(βX) mathclose: ), where X is a log-correlated Gaussian field. Our construction applies on bounded convex domains for every particle activity α∈ℝ and throughout the subcritical range β2∈[0,4), below the Berezinskii-Kosterlitz-Thouless threshold. We apply the martingale method introduced by Lacoin, Rhodes and Vargas to two dimensions by using refined estimates based on charge conjugation symmetries. Our result extends existing constructions by treating the full subcritical regime for a broad class of covariances.
Related
- Form factors of field exponentials in the 1+1 dimensional Sine-Gordon model
- Wronskian representations of the solutions to the sine-Gordon equation
- An integrable deformation of the sine(sinh)-Gordon model -- Non-Lie algebra
- Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence
- Tropical QFT and the sine-Gordon model
BibTeX
@misc{bonnefont2026probabilistic,
title = {{Probabilistic ultraviolet renormalization of the two-dimensional Sine-Gordon model}},
author = {Benjamin Bonnefont and Hermanni Rajamäki and Vincent Vargas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32927},
eprint = {2610.32927},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32927},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Probabilistic ultraviolet renormalization of the two-dimensional Sine-Gordon model
AU - Benjamin Bonnefont
AU - Hermanni Rajamäki
AU - Vincent Vargas
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32927
UR - https://arxiv.org/abs/2610.32927
AB - We give a probabilistic approach to the ultraviolet renormalization of the two-dimensional Sine-Gordon model. The model is formally described by the density exp(α∫ mathopen: cos(βX) mathclose: ), where X is a log-correlated Gaussian field. Our construction applies on bounded convex domains for every particle activity α∈ℝ and throughout the subcritical range β^2∈[0,4), below the Berezinskii-Kosterlitz-Thouless threshold. We apply the martingale method introduced by Lacoin, Rhodes and Vargas to two dimensions by using refined estimates based on charge conjugation symmetries. Our result extends existing constructions by treating the full subcritical regime for a broad class of covariances.
ER -