On Chern-Simons Quivers and Toric Geometry

TL;DR

This paper explores the relationship between 3D N=4 Chern-Simons quiver gauge theories and toric geometry, specifically how constraints on CS levels relate to toric equations of hyper-Kahler manifolds derived from Fano varieties.

Contribution

It establishes a connection between Chern-Simons quiver models and toric geometry, providing explicit geometric interpretations of gauge theory constraints.

Findings

CS levels are related to toric equations of V^2.

Quiver diagrams encode the geometry of hyper-Kahler manifolds.

The approach links M-theory compactifications to toric geometry.

Abstract

We discuss a class of 3-dimensional N=4 Chern-Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex 4-dimensional hyper-Kahler (HK) manifolds, which are realized explicitly as a cotangent bundle over two-Fano toric varieties V^2. The corresponding CS gauge models are encoded in quivers similar to toric diagrams of V^2. Using toric geometry, it is shown that the constraints on CS levels can be related to toric equations determining V^2.