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

Abstract

We briefly review a class of four dimensional $\mathcal{N}=3$ field theories constructed by taking a quotient of $\mathcal{N}=4$ SYM with gauge group $U(N)$. The quotient involves a discrete symmetry that only exists for specific, order one, values of the coupling constant, so the resulting theories are intrinsically strongly coupled. These theories admit a simple realization in string theory as the worldvolume theory of a stack of D3 branes probing a generalized orientifold plane, or S-fold. Their holographic dual is given by a non-trivial F-theory fibration over $Ad{S}_5\times S^5/{\mathbb{Z}}_k$ which is weakly curved but with the string coupling frozen at an order one value.

Proceedings prepared for the "Workshop on Geometry and Physics", November 2016, Ringberg Castle, Germany