Geometric Transitions and D-Term SUSY Breaking

TL;DR

This paper introduces a geometric approach using transitions in Calabi-Yau manifolds to analyze metastable supersymmetry-breaking vacua in string and gauge theories, linking geometric configurations to gauge theory phenomena.

Contribution

It develops a novel geometric framework connecting D-brane configurations and fluxes to metastable SUSY-breaking vacua in N=2 gauge theories deformed to N=1.

Findings

Geometric engineering of SUSY-breaking vacua via D5 branes on rigid 2-cycles.

Dual Calabi-Yau geometries with fluxes represent non-supersymmetric confining vacua.

Effective use of geometric transitions to study metastable states.

Abstract

We propose a new way of using geometric transitions to study metastable vacua in string theory and certain confining gauge theories. The gauge theories in question are N=2 supersymmetric theories deformed to N=1 by superpotential terms. We first geometrically engineer supersymmetry-breaking vacua by wrapping D5 branes on rigid 2-cycles in noncompact Calabi-Yau geometries, such that the central charges of the branes are misaligned. In a limit of slightly misaligned charges, this has a gauge theory description, where supersymmetry is broken by Fayet-Iliopoulos D-terms. Geometric transitions relate these configurations to dual Calabi-Yaus with fluxes, where H_RR, H_NS and dJ are all nonvanishing. We argue that the dual geometry can be effectively used to study the resulting non-supersymmetric, confining vacua.