Calabi-Yau fourfolds with flux and supersymmetry breaking

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.

The effective action of Calabi–Yau orientifolds

“…In this way we will be able to understand the definition of the Kähler coordinates given in (3.25) as a superfield duality transformation and furthermore discover the no-scale property (3.29) of K k somewhat more conceptually. In an analog three-dimensional situation this has also been observed in [24].…”

Onα′corrections inN=1F-theory compactifications

“…Both only depend on the Kähler moduli of the N = 1 reduction. The presence of a volume correction in the M-theory reduction on Calabi-Yau fourfolds has already been stressed in [10,11]. We find here that, due to this correction, the right 4d, N = 1 coordinates are shifted from their classical value.…”

“…The correction is given by a Lorentz invariant combination of four powers of the Riemann tensor R (11) of the schematic form…”

The Ramond–Ramond sector of string theory beyond leading order

“…They have also been argued to lead to induced Einstein-Hilbert terms, which are important for gravity localisation phenomena [4,5] as they arise in brane-world scenarios. Furthermore, they may play a role in supersymmetry breaking [6,7] by producing a potential that stabilises certain moduli for nonsupersymmetric vacua. In black-hole and black-brane physics, higher-derivative terms lead to modifications of the thermodynamics, and thus implicitly to new tests of the string-theory description of the entropy of such objects [8,9].…”