Calabi-Yau fourfolds with flux and supersymmetry breaking

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.