A simple class of N=3 gauge/gravity duals

TL;DR

This paper constructs gravity duals for an infinite series of N=3 Chern-Simons quiver theories using M-theory compactifications on specific 3-Sasaki-Einstein manifolds, linking field theory and geometry.

Contribution

It introduces a new class of M-theory AdS_4 x M_7 vacua with explicit geometric descriptions for N=3 Chern-Simons quiver theories.

Findings

Identified gravity duals for an infinite series of N=3 theories.

Described the geometry of M_7 manifolds via hyperKaehler toric fans.

Connected these theories to four-dimensional N=1 theories with similar quivers.

Abstract

We find the gravity duals to an infinite series of N=3 Chern-Simons quiver theories. They are AdS_4 x M_7 vacua of M-theory, with M_7 in a certain class of 3-Sasaki-Einstein manifolds obtained by a quotient construction. The field theories can be engineered from a brane configuration; their geometry is summarized by a "hyperKaehler toric fan" that can be read off easily from the relative angles of the branes. The singularity at the tip of the cone over M_7 is generically not an orbifold. The simplest new manifolds we consider can be written as the biquotient U(1)\U(3)/U(1). We also comment on the relation between our theories and four-dimensional N=1 theories with the same quiver.