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arXiv · 2503.21326

Operator product expansions of derivative fields in the sine-Gordon model

Alex Karrila·Tuomas Virtanen·Christian Webb
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Abstract

In this article, we initiate the study of operator product expansions (OPEs) for the sine-Gordon model. For simplicity, we focus on the model below the first threshold of collapse ($\beta<4\pi$) and on the singular terms in OPEs of derivative-type fields $\partial \varphi$ and $\bar\partial\varphi$. We prove that compared to corresponding free field OPEs, the sine-Gordon OPEs develop logarithmic singularities and generate Wick ordered exponentials. Our approach for proving the OPEs relies heavily on Onsager-type inequalities and associated moment bounds for GFF correlation functions involving Wick ordered exponentials of the free field.

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Alex Karrila, Tuomas Virtanen, Christian Webb. 2025-03-27. Operator product expansions of derivative fields in the sine-Gordon model. https://doi.org/10.1007/s10955-026-03585-3

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