Renormalization of the Periodic Scalar Field Theory by Polchinski's Renormalization Group Method

TL;DR

This paper investigates the renormalization group flow of the two-dimensional sine-Gordon model using Polchinski's method, examining scheme dependence and extending beyond local potential approximation to clarify wave-function renormalization effects.

Contribution

It compares different RG schemes for the sine-Gordon model and extends the analysis beyond local potential approximation to study wave-function renormalization.

Findings

Recovered the Coleman fixed point after linearization.

Flow shows strong scheme dependence with non-linear terms.

Compared RG flow with Wegner-Houghton and Coulomb-gas approaches.

Abstract

The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this work we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas.