Geometric regularizations and dual conifold transitions

TL;DR

This paper introduces a geometric regularization method for conifold transitions in noncompact Calabi-Yau spaces, preserving SL(2,Z) invariance and enabling period computations via Picard-Fuchs equations, with applications to D-brane systems and flux backgrounds.

Contribution

It presents a novel regularization technique that maintains symmetries and simplifies period calculations in conifold transitions, linking D-brane systems to flux backgrounds.

Findings

Regularization respects SL(2,Z) invariance.

Allows computation of periods via Picard-Fuchs equations.

Provides insights into local conifold and flux backgrounds.

Abstract

We consider a geometric regularization for the class of conifold transitions relating D-brane systems on noncompact Calabi-Yau spaces to certain flux backgrounds. This regularization respects the SL(2,Z) invariance of the flux superpotential, and allows for computation of the relevant periods through the method of Picard-Fuchs equations. The regularized geometry is a noncompact Calabi-Yau which can be viewed as a monodromic fibration, with the nontrivial monodromy being induced by the regulator. It reduces to the original, non-monodromic background when the regulator is removed. Using this regularization, we discuss the simple case of the local conifold, and show how the relevant field-theoretic information can be extracted in this approach.