I will present the first examples of N=3 field theories in four dimensions, obtained by quotienting N=4 SYM by particular combinations of R-symmetry and SL(2,Z) duality symmetries. These theories have a simple embedding in string theory which allows to analyze some of their most basic properties. I will discuss their large N limit and propose an alternative construction in terms of the (2,0) theory in six dimensions. Finally, I will mention some generalizations.

MPI Munich