F-theory and N=1 Quivers from Polyvalent Geometry

TL;DR

This paper explores four-dimensional N=1 quiver gauge theories derived from F-theory compactifications on hyper-Kähler fourfolds, emphasizing the role of intersecting toric surfaces and local Calabi-Yau equations in satisfying physical constraints.

Contribution

It introduces a novel class of N=1 quiver models with fundamental matter using polyvalent toric geometry and demonstrates how local Calabi-Yau equations ensure anomaly cancellation.

Findings

Constructed linear chains of SU(N) gauge groups with flavor symmetries.

Demonstrated the use of intersecting complex toric surfaces in model building.

Showed how local Calabi-Yau equations solve physical constraints.

Abstract

We study four dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K\"{a}hler structure. Using intersecting complex toric surfaces, we derive a class of N=1 quivers with charged fundamental matter placed on external nodes. The emphasis is on how local Calabi-Yau equations solve the corresponding physical constraints including the anomaly cancelation condition. Concretely, a linear chain of SU(N) groups with flavor symmetries has been constructed using polyvalent toric geometry.