Hard Non-commutative Loops Resummation

TL;DR

This paper proves the all-order ultraviolet renormalizability of a non-commutative Euclidean $g^2\phi^4$ theory using Wilsonian flow equations and develops a resummation method for infrared divergences similar to Hard Thermal Loops, with explicit NLO corrections.

Contribution

It introduces a non-commutative $g^2\phi^4$ theory framework and applies a novel resummation technique for infrared divergences, extending the understanding of non-commutative quantum field theories.

Findings

Ultraviolet renormalizability proved to all orders.

Infrared divergences require resummation similar to thermal field theory.

Next-to-leading order corrections computed explicitly.

Abstract

The non-commutative version of the euclidean $g^2\phi^4$ theory is considered. By using Wilsonian flow equations the ultraviolet renormalizability can be proved to all orders in perturbation theory. On the other hand, the infrared sector cannot be treated perturbatively and requires a resummation of the leading divergencies in the two-point function. This is analogous to what is done in the Hard Thermal Loops resummation of finite temperature field theory. Next-to-leading order corrections to the self-energy are computed, resulting in $O(g^3)$ contributions in the massless case, and $O(g^6\log g^2)$ in the massive one.