M2-Branes and Fano 3-folds

TL;DR

This paper explores supersymmetric gauge theories from M2-branes probing Calabi-Yau 4-folds over Fano 3-folds, deriving their moduli space data, generators, and operator dimensions.

Contribution

It introduces a systematic method to analyze the mesonic moduli space of these theories using toric data, Hilbert series, and the forward algorithm.

Findings

Toric data of mesonic moduli spaces are derived for each model.

Generators of the mesonic moduli space are explicitly determined.

Scaling dimensions of chiral operators are computed.

Abstract

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.