The fate of the Wilson-Fisher fixed point in non-commutative \phi^4

TL;DR

This paper investigates the behavior of the Wilson-Fisher fixed point in a non-commutative ^4 theory, revealing a transition between a known fixed point and a new strongly interacting fixed point due to non-commutativity effects.

Contribution

It introduces a detailed analysis of the non-commutative Wilson-Fisher fixed point and identifies a novel strongly interacting fixed point influenced by maximal non-commutativity.

Findings

The non-commutative Wilson-Fisher fixed point interpolates between the commutative fixed point and a new strongly interacting fixed point.

The fixed point structure depends on the degree of non-commutativity, with a transition at maximal non-commutativity.

The theory exhibits a two-sheeted structure of the critical coupling as a function of the dilation parameter.

Abstract

In this article we study non-commutative vector sigma model with the most general \phi^4 interaction on Moyal-Weyl spaces. We compute the 2- and 4-point functions to all orders in the large N limit and then apply the approximate Wilson renormalization group recursion formula to study the renormalized coupling constants of the theory. The non-commutative Wilson-Fisher fixed point interpolates between the commutative Wilson-Fisher fixed point of the Ising universality class which is found to lie at zero value of the critical coupling constant a_* of the zero dimensional reduction of the theory, and a novel strongly interacting fixed point which lies at infinite value of a_* corresponding to maximal non-commutativity beyond which the two-sheeted structure of a_* as a function of the dilation parameter disappears.