On toric geometry, Spin(7) manifolds, and type II superstring compactifications

TL;DR

This paper explores the geometry of Spin(7) manifolds used in type II superstring compactifications, utilizing toric methods to analyze their structure, transitions, and dualities, with implications for higher-dimensional theories.

Contribution

It introduces a toric construction of Spin(7) manifolds as intersecting Calabi-Yau conifolds and discusses geometric transitions and brane/flux dualities in this context.

Findings

Toric realization of Spin(7) manifolds as intersecting Calabi-Yau conifolds

Analysis of geometric transitions in Spin(7) manifolds

Discussion of brane/flux duality in string compactifications

Abstract

We consider type II superstring compactifications on the singular Spin(7) manifold constructed as a cone on SU(3)/U(1). Based on a toric realization of the projective space CP^2, we discuss how the manifold can be viewed as three intersecting Calabi-Yau conifolds. The geometric transition of the manifold is then addressed in this setting. The construction is readily extended to higher dimensions where we speculate on possible higher-dimensional geometric transitions. Armed with the toric description of the Spin(7) manifold, we discuss a brane/flux duality in both type II superstring theories compactified on this manifold.