Del Pezzo singularities and SUSY breaking

TL;DR

This paper constructs compact Calabi-Yau manifolds with del Pezzo singularities, analyzes their deformations, and explores their potential for dynamical SUSY breaking mechanisms, including explicit ISS vacua.

Contribution

It provides explicit constructions of Calabi-Yau manifolds with del Pezzo singularities and examines their role in SUSY breaking, including detailed examples and mechanisms.

Findings

Constructed complete intersection CY manifolds with del Pezzo singularities.

Analyzed complex deformations of these singularities.

Presented an explicit ISS vacuum example for del Pezzo 6 singularity.

Abstract

An analytic construction of compact Calabi-Yau manifolds with del Pezzo singularities is found. We present complete intersection CY manifolds for all del Pezzo singularities and study the complex deformations of these singularities. An example of the quintic CY manifold with del Pezzo 6 singularity and some number of conifold singularities is studied in details. The possibilities for the 'geometric' and ISS mechanisms of dynamical SUSY breaking are discussed. As an example, we construct the ISS vacuum for the del Pezzo 6 singularity.