$\mathcal N=3$ four dimensional field theories

TL;DR

This paper reviews four-dimensional $ =3$ supersymmetric field theories obtained from $ =4$ SYM via discrete quotients, highlighting their string theory realization and holographic duals involving F-theory fibrations.

Contribution

It introduces a class of $ =3$ theories constructed from $ =4$ SYM, detailing their string theory realization and holographic duals, which are intrinsically strongly coupled.

Findings

Theories are realized as D3 branes probing generalized orientifolds or S-folds.

Holographic duals involve F-theory fibrations over $AdS_5 \times S^5/\mathbb{Z}_k$.

String coupling is frozen at an order one value, indicating strong coupling.

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 $AdS_5 \times S^5/\mathbb Z_k$ which is weakly curved but with the string coupling frozen at an order one value.