Renormalization and Induced Gauge Action on a Noncommutative Space
arXiv:0706.2167 · doi:10.1143/PTPS.171.161
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 $Ï^3$ models and use heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $θ$-deformed space and derive noncommutative gauge actions.
20 pages; to appear in the proceedings of the 21st Nishinomiya-Yukawa Memorial Symposium Noncommutative geometry and quantum spacetime in physics, Nishinomiya and Kyoto (Japan), 2006