Renormalization and Induced Gauge Action on a Noncommutative Space

Understand

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.