Calabi-Yau Fourfolds with Flux and Supersymmetry Breaking

TL;DR

This paper explores how fluxes in Calabi-Yau fourfolds within M-theory can lead to partial supersymmetry breaking, providing new conditions and examples for N=2 to N=1 breaking in three-dimensional theories.

Contribution

It introduces new conditions for supersymmetry breaking in Calabi-Yau fourfold compactifications and provides an explicit example satisfying these conditions.

Findings

Recovered known results for unbroken N=2 supersymmetry.

Derived a new condition for breaking N=2 to N=1 supersymmetry.

Presented an example of a Calabi-Yau hypersurface satisfying the breaking condition.

Abstract

In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of general N=2 gauged supergravities, in the special case where only translational symmetries are gauged. This allows us to extract supersymmetry-breaking conditions, and interpret them as conditions on the 4-form flux and Calabi-Yau geometry. For N=2 unbroken supersymmetry in three dimensions we recover previously known results, and we find a new condition for breaking supersymmetry from N=2 to N=1, i.e. from four to two supercharges. An example of a Calabi-Yau hypersurface in a toric variety that satisfies this condition is provided.