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

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.