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Mass gap for the hierarchical sinh-Gordon model
Abstract
The (massless) sinh-Gordon model is defined in terms of a continuum massless Gaussian free field perturbed by a cosh interaction. For the hierarchical version of the model, we prove existence of the infinite volume limit, a uniform log-Sobolev inequality, and a mass gap. Our results hold for all b2 ∈ (0,1) and simplify for b2 ∈ (0,1/2) for which the Gaussian multiplicative chaos has two moments. In an appendix, our renormalization group analysis is compared with the conjectures and controversies in physics which are mostly based on formal analytic continuation of conjectures for the sine-Gordon model and we raise some questions.
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BibTeX
@misc{abdelghani2026mass,
title = {{Mass gap for the hierarchical sinh-Gordon model}},
author = {Omar Abdelghani and Roland Bauerschmidt and Michael Hofstetter and Ofer Zeitouni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17461},
eprint = {2609.17461},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17461},
}
RIS
TY - UNPB
TI - Mass gap for the hierarchical sinh-Gordon model
AU - Omar Abdelghani
AU - Roland Bauerschmidt
AU - Michael Hofstetter
AU - Ofer Zeitouni
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17461
UR - https://arxiv.org/abs/2609.17461
AB - The (massless) sinh-Gordon model is defined in terms of a continuum massless Gaussian free field perturbed by a cosh interaction. For the hierarchical version of the model, we prove existence of the infinite volume limit, a uniform log-Sobolev inequality, and a mass gap. Our results hold for all b^2 ∈ (0,1) and simplify for b^2 ∈ (0,1/2) for which the Gaussian multiplicative chaos has two moments. In an appendix, our renormalization group analysis is compared with the conjectures and controversies in physics which are mostly based on formal analytic continuation of conjectures for the sine-Gordon model and we raise some questions.
ER -