A simple class of N=3 gauge/gravity duals

TL;DR

This work constructs a broad class of AdS$_4$/CFT$_3$ duals for ${\cal N}=3$ Chern-Simons quiver theories by identifying their M-theory moduli spaces as hyperKähler quotients and matching them to near-horizon geometries $AdS_4\times M_7$ with $M_7$ 3-Sasakian. The authors introduce the hypertoric fan description, derive explicit abelian moduli spaces (including the biquotient $U(1)\backslash U(3)/U(1)$), and connect brane configurations to the geometry, clarifying when the cone tip is non-orbifold. They relate the 3d moduli spaces to 4d quiver theories, explore orientifold extensions, and provide concrete brane-engineering and duality frameworks that yield a robust AdS$_4$/CFT$_3$ dictionary with rich geometric structure such as Eschenburg spaces. Overall, the paper broadens the landscape of well-controlled AdS$_4$/CFT$_3$ examples and offers a geometric toolkit (hyperKähler quotients and hypertoric fans) for constructing and interpreting these dualities.

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.

Figures (3)

• Figure 1: The quiver.
• Figure 2: The vectors $u_i$ of the "hypertoric fan".
• Figure 3: A cartoon of the brane configuration.