Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories

TL;DR

This paper introduces a novel method using dimer models to identify gravity duals for a broad class of 3D Chern-Simons-matter theories, linking them to toric Calabi-Yau four-folds in M-theory.

Contribution

It presents a new approach to determine gravity duals for Chern-Simons-matter theories via toric geometry and dimer models, expanding the toolkit for gauge/gravity duality.

Findings

Establishes a correspondence between Chern-Simons-matter theories and toric Calabi-Yau 4-folds.

Provides a method to construct gravity duals using dimer model techniques.

Shows that the moduli space matches the cone over a toric Sasaki-Einstein manifold.

Abstract

We propose a new method to find gravity duals to a large class of three-dimensional Chern-Simons-matter theories, using techniques from dimer models. The gravity dual is given by M-theory on AdS_4\times Y_7, where Y_7 is an arbitrary seven-dimensional toric Sasaki-Einstein manifold. The cone of Y_7 is a toric Calabi-Yau 4-fold, which coincides with a branch of the vacuum moduli space of Chern-Simons-matter theories.