N=3 four dimensional field theories

We introduce a class of four dimensional field theories constructed by quotienting ordinary N = 4 U(N) SYM by particular combinations of R-symmetry and SL(2; Z) automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large N limit described by a non-trivial F-theory fibration with base AdS(5) x (S-5/Z(k)). Upon reduction on a circle the N = 3 theories flow to well-known N = 6 ABJM theories.