Noncommutative QFT and Renormalization

TL;DR

This paper reviews methods to address IR/UV mixing in noncommutative quantum field theories, demonstrating renormalization solutions, applications to scalar models, and deriving gauge actions on deformed spaces.

Contribution

It introduces a novel approach to cure IR/UV mixing by adding a marginal operator and applies heat kernel techniques to derive noncommutative gauge actions.

Findings

Successful renormalization of certain noncommutative models

Application of heat kernel methods to gauge theories on deformed spaces

Derivation of noncommutative gauge field actions

Abstract

Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to $\phi^3$ models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $\theta$-deformed space and derive noncommutative gauge field actions.