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

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 $\partial \phi$ and $\bar{\partial }\phi$. 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.