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

TL;DR

This paper derives explicit short-distance expansions of correlation functions in the sine-Gordon model across all coupling regimes, using conformal perturbation theory and novel regularization techniques, connecting to Ising and Gross-Neveu models.

Contribution

It introduces a new regularization method to evaluate integral expressions for correlation functions in the sine-Gordon theory at all couplings, linking to known critical models.

Findings

Explicit integral expressions for correlation functions at all orders.

Connections to Ising and Gross-Neveu models at critical points.

Recovery of known critical expansions and flow behaviors.

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.