Geometric Transition versus Cascading Solution

TL;DR

This paper compares Vafa's geometric transition and the Klebanov-Strassler solution within M-theory, establishing their equivalence through brane configurations and exploring their realization as fourfolds with G-fluxes, including potential non-supersymmetric extensions.

Contribution

It provides a detailed analysis of the equivalence between two major models in string theory and explores their realization as fourfolds with fluxes, extending to non-supersymmetric cases.

Findings

Demonstrated equivalence between geometric transition and cascading solution

Identified fourfold realizations with G-fluxes in certain limits

Discussed potential non-supersymmetric extensions

Abstract

We study Vafa's geometric transition and Klebanov - Strassler solution from various points of view in M-theory. In terms of brane configurations, we show the detailed equivalences between the two models. In some limits, both models have an alternative realization as fourfolds in M-theory with appropriate G-fluxes turned on. We discuss some aspects of the fourfolds including how to see the transition and a possible extension to the non-supersymmetric case.