Gauge fields on non‐commutative spaces and renormalization

Abstract

Constructing renormalizable models on non‐commutative spaces constitutes a big challenge. Only few examples of renormalizable theories are known, such as the scalar Grosse‐Wulkenhaar model. Gauge fields are even more difficult, since new renormalization techniques are required which are compatible with the inherently non‐local setting on the one hand, and also allow to properly treat the gauge symmetry on the other hand. In this proceeding (which is based on my talk given at the “Workshop on Noncommutative Field Theory and Gravity” in Corfu/Greece, September 8–15, 2013), I focus on this last point and present new extensions to existing renormalization schemes (which are known to work for gauge field theories in commutative space) adapted to non‐commutative Moyal space.

Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model

“…It would be interesting to see if similar conclusions could be reached in fuzzy de Sitter space as well [17,18]. UV/IR mixing still poses a problem for gauge fields on NC spaces [19]. Hoping to build on the GW model's success, [20,21] tried to adapt it to a gauge field on h tr .…”