Gauge Theory on Non(anti)commutative Superspaces

One of the basic problems of quantum field theories, namely the ultraviolet infinities, is connected to the fact that we consider point particles and spaces which allow the definition of points. The infinities which arise in the gauge theories of the strong and electroweak interactions can be removed by a procedure called renormalization. However, the quantum field theory of gravity is not renormalizable. This is the reason why we say that quantum mechanics and general relativity are not compatible. Although supersymmetry improves its renormalization properties, the theory of supergravity is still not renormalizable. Following the history of unification we could think about circumventing the problem of ultraviolet infinities by dramatically changing spacetime. For example, one could assume that at a sufficiently small fundamental length the spacetime is noncommutative. On such spacetimes the definition of points doesn't make sense.
In the present work the author consider gauge theories on non(anti)commutative superspaces. Different construction methods and related problems of these theories are discussed. In particular, the incompatibility of the Seiberg-Witten map with the (anti)chirality, locality and supersymmetry at the same time is demonstrated. Phenomenologically interesting actions are also presented.