N = 3 $$ \mathcal{N}=3 $$ four dimensional field theories

Abstract

We introduce a class of four dimensional field theories constructed by quotienting ordinary $$ \mathcal{N}=4 $$ 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 × (S 5/ℤ k ). Upon reduction on a circle the $$ \mathcal{N}=3 $$ theories flow to well-known $$ \mathcal{N}=6 $$ ABJM theories.