Quiver Gauge theories from Lie Superalgebras

TL;DR

This paper explores quiver gauge theories derived from Lie superalgebras, particularly focusing on the A(1,0) case, and demonstrates how toric geometry can incorporate fundamental fields into these models.

Contribution

It introduces a novel approach linking Lie superalgebra-based quiver gauge models with toric geometry, expanding the framework to include fundamental matter fields.

Findings

A(1,0) quivers relate to intersecting complex cycles with genus g.

Toric geometry enables incorporation of fundamental fields into product gauge groups.

Potential extension of methods to other Lie superalgebras.

Abstract

We discuss quiver gauge models with matter fields based on Dynkin diagrams of Lie superalgebra structures. We focus on A(1,0) case and we find first that it can be related to intersecting complex cycles with genus $g$. Using toric geometry, A(1,0) quivers are analyzed in some details and it is shown that A(1,0) can be used to incorporate fundamental fields to a product of two unitary factor groups. We expect that this approach can be applied to other kinds of Lie superalgebras;