Renormalization and Induced Gauge Action on a Noncommutative Space

TL;DR

This paper discusses how to address renormalization issues in noncommutative field theories by adding a marginal operator, applying these ideas to scalar models, and deriving noncommutative gauge actions using heat kernel methods.

Contribution

It introduces a method to cure IR/UV mixing in noncommutative theories by adding a marginal operator and applies it to scalar and gauge field models.

Findings

Successful application to $$ models

Derivation of noncommutative gauge actions

Use of heat kernel expansion methods

Abstract

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