Flux compactification on smooth, compact three-dimensional toric varieties

TL;DR

This paper develops methods to construct G-structures on smooth, compact three-dimensional toric varieties, enabling systematic exploration of supersymmetric flux compactifications in string theory.

Contribution

It introduces techniques for constructing G-structures on SCTV and analyzing their torsion classes, with explicit examples including infinite classes of toric CP^1 bundles.

Findings

Methods for constructing G-structures on SCTV

Explicit examples of G-structures on toric varieties

Potential for systematic study of flux vacua

Abstract

Three-dimensional smooth, compact toric varieties (SCTV), when viewed as real six-dimensional manifolds, can admit G-structures rendering them suitable for internal manifolds in supersymmetric flux compactifications. We develop techniques which allow us to systematically construct G-structures on SCTV and read off their torsion classes. We illustrate our methods with explicit examples, one of which consists of an infinite class of toric CP^1 bundles. We give a self-contained review of the relevant concepts from toric geometry, in particular the subject of the classification of SCTV in dimensions less or equal to 3. Our results open up the possibility for a systematic construction and study of supersymmetric flux vacua based on SCTV.