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 (β 4 π) and on the singular terms in OPEs of derivative-type fields ∂ φ and ∂ ¯ φ. 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.
Karrila et al. (Mon,) studied this question.