Matter from Toric Geometry

TL;DR

This paper introduces an algorithm to determine the matter content of 6D theories from F-theory compactifications on elliptic Calabi-Yau threefolds within toric varieties, utilizing polyhedral data and anomaly cancellation.

Contribution

It provides a novel, systematic method to extract matter content directly from the toric data of Calabi-Yau hypersurfaces in F-theory compactifications.

Findings

Algorithm successfully computes matter content from polyhedra.

Method aligns with anomaly cancellation conditions.

Applicable to a wide class of toric Calabi-Yau threefolds.

Abstract

We present an algorithm for obtaining the matter content of effective six-dimensional theories resulting from compactification of F-theory on elliptic Calabi-Yau threefolds which are hypersurfaces in toric varieties. The algorithm allows us to read off the matter content of the theory from the polyhedron describing the Calabi-Yau manifold. This is based on the generalized Green-Schwarz anomaly cancellation condition.