Brane Tilings and M2 Branes

TL;DR

This paper explores the use of brane tilings to efficiently describe N=2 Chern-Simons-matter theories related to M2-branes on toric Calabi-Yau fourfolds, introducing a modified Kasteleyn technique and analyzing spectra via Hilbert Series.

Contribution

It introduces a simple modification of the Kasteleyn technique to compute three-dimensional toric diagrams for M2-brane moduli spaces.

Findings

Modified Kasteleyn technique successfully computes toric diagrams.

Hilbert Series analysis reveals spectrum of scaling dimensions.

Method applies to non-compact moduli spaces of M2-branes.

Abstract

Brane tilings are efficient mnemonics for Lagrangians of N=2 Chern-Simons-matter theories. Such theories are conjectured to arise on M2-branes probing singular toric Calabi-Yau fourfolds. In this paper, a simple modification of the Kasteleyn technique is described which is conjectured to compute the three dimensional toric diagram of the non-compact moduli space of a single probe. The Hilbert Series is used to compute the spectrum of non-trivial scaling dimensions for a selected set of examples.