Short Distance Expansions of Correlation Functions in the Sine-Gordon Theory

Abstract

We examine the two-point correlation functions of the fields exp(i$\alpha\Phi$) in the sine-Gordon theory at all values of the coupling constant $\hat\beta$. Using conformal perturbation theory, we write down explicit integral expressions for every order of the short distance expansion. Using a novel technique analagous to dimensional regularisation, we evaluate these integrals for the first few orders finding expressions in terms of generalised hypergeometric functions. From these derived expressions, we examine the limiting forms at the points where the sine-Gordon theory maps onto a doubled Ising and the Gross-Neveu SU(2) models. In this way we recover the known expansions of the spin and disorder fields about criticality in the Ising model and the well known Kosterlitz-Thouless flows in the Gross-Neveu SU(2) model.