Aharony Evtikhiev on 4d N=3 SCFT 4d N=3 vector multiplet decomposes into 4d N=2 vector and hyper. 4d N=3 SCFTs obey a=c and have no (4d N=3) relevant deformation. The existence of a (4d N=3) global non-R symmetry or (4d N=2) exactly marginal deformation implies 4d N=4 susy. The moduli space is always a "Coulomb branch"; there are constraints on possible dimensions of operators labeling it.
García-Etxebarria Regalado construct 4d N=3 orbifolds of 4d N=4 Quotient of 4d N=4 by combination of R-symmetry and SL(2,Z) automorphism, which only makes sense for self-dual coupling \tau, thus killing exactly marginal deformations. From F-theory point of view, this is similar to an O3 plane, but where the orbifold acts on T^2 (i.e., on the axiodilaton). The theory dimensionally reduces to ABJM. The paper also contains an interesting description of global aspects of the gauge group with an O3 plane.
Beck Gutowski Papadopoulos 24 susy AdS5 backgrounds. Gravitational duals to 4d N=3 SCFTs must be singular or have non-compact internal space. True in IIA sugra (provided the homogeneity conjecture holds) and in IIB sugra.