Effective Field Theories on Non-Commutative Space-Time

Abstract

We consider Yang-Mills theories formulated on a non-commutative space-time described by a space-time dependent anti-symmetric field $θ^{μν}(x)$. Using Seiberg-Witten map techniques we derive the leading order operators for the effective field theories that take into account the effects of such a background field. These effective theories are valid for a weakly non-commutative space-time. It is remarkable to note that already simple models for $θ^{μν}(x)$ can help to loosen the bounds on space-time non-commutativity coming from low energy physics. Non-commutative geometry formulated in our framework is a potential candidate for new physics beyond the standard model.