N=3 four dimensional field theories

TL;DR

This paper introduces four-dimensional field theories derived from $ ext{N}=4$ SYM via quotienting by R-symmetry and $SL(2,bZ)$ automorphisms, related to D3 branes in F-theory, with fixed coupling and novel large N behavior.

Contribution

It constructs new $ ext{N}=3$ theories from $ ext{N}=4$ SYM using automorphisms, revealing their connection to F-theory and known $ ext{N}=6$ ABJM theories upon reduction.

Findings

Theories have fixed coupling of order one.

Large N limit described by F-theory fibration.

Reduction leads to $ ext{N}=6$ ABJM 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 $SL(2,\mathbb{Z})$ 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 $AdS_5\times (S^5/\mathbb{Z}_k)$. Upon reduction on a circle the $\mathcal{N}=3$ theories flow to well-known $\mathcal{N}=6$ ABJM theories.