Stress tensor correlations and the c-theorem in models with exponential interactions

Abstract

We study the scaling properties of models of the sine-Gordon type with exponential interactions γ + exp( iλφ) + γ − exp(− iλφ) in the presence of a background charge. In the Kosterlitz-Thouless region λ 2 ∼ 4, where wave-function renormalization is required, we compute to second order in γ +, γ − the two-point correlation functions of the stress tensor, and the corresponding Zamolodchikov c-function. Their behavior under scaling is affected by infrared effects. However, in the λ 2 ∼ 4 region they have smooth limits as the infrared cut-off is removed and in this limit the usual properties of the c-function are recovered. By comparing our results to those of Zamolodchikov we argue that the renormalization group flows of the coupling constants are controlled by generalized β̃ functions. We solve the flow equations and relate our results to those found in perturbed minimal models.