Fractional branes and the gravity dual of partial supersymmetry breaking

TL;DR

This paper explores how fractional D3-branes in string theory create a gravity dual that models partial supersymmetry breaking and geometric transitions, linking orbifold singularities to smooth Calabi-Yau geometries.

Contribution

It provides a detailed gravity dual description of partial supersymmetry breaking via fractional branes and connects orbifold resolutions to geometric transitions in string theory.

Findings

Gravity dual of non-trivial potential on Coulomb branch

Spontaneous partial supersymmetry breaking in resolved geometries

Emergence of the resolved conifold geometry

Abstract

In type IIB string theory, we consider fractional D3-branes in the orbifold background dual to four-dimensional N=2 supersymmetric Yang-Mills theory. We find the gravitational dual description of the generation of a non-trivial field theory potential on the Coulomb branch. When the orbifold singularity is softened to the smooth Eguchi-Hanson space, the resulting potential induces spontaneous partial supersymmetry breaking. We study the N=1 theory arising in those vacua and we see how the resolved conifold geometry emerges in this way. It will be natural to identify the size of the blown-up two-cycle of that geometry with the inverse mass of the adjoint chiral scalar. We finally discuss the issue of geometric transition in this context.