On Geometric Transitions in String Compactifications

TL;DR

This paper explores geometric transitions and brane/flux dualities across various string theory compactifications, providing toric and F-theory interpretations, and examining their implications in different dimensions with preserved supersymmetry.

Contribution

It offers new toric and F-theory perspectives on geometric transitions in Calabi-Yau and Spin(7) manifolds, connecting them with dualities and mirror symmetry.

Findings

Toric interpretations of topology-changing transitions in Calabi-Yau and Spin(7) manifolds.

A four-dimensional F-theory interpretation of type IIB geometric transitions.

Analysis of brane/flux duality in Spin(7) compactifications with ${ m N}=1/2$ supersymmetry.

Abstract

We reconsider the study of the geometric transitions and brane/flux dualities in various dimensions. We first give toric interpretations of the topology changing transitions in the Calabi-Yau conifold and the $Spin(7)$ manifold. The latter, for instance, can be viewed as three intersecting Calabi-Yau conifolds according to $\cp^2$ toric graph. Orbifolds of such geometries are given in terms of del Pezzo complex surfaces. Second we propose a four-dimensional F-theory interpretation of type IIB geometric transitions on the Calabi-Yau conifold. This gives a dual description of the M-theory flop in terms of toric mirror symmetry. In two dimensions, we study the geometric transition in a singular $Spin(7)$ manifold constructed as a cone on SU(3)/U(1). In particular, we discuss brane/flux duality in such a compactification in both type IIA and type IIB superstrings. These examples preserve one supercharge and so have ${\cal N}= 1/2$ supersymmetry in two dimensions. Then, an interpretation in terms of F-theory is given.