Supersymmetric compactifications of heterotic strings with fluxes and condensates

Abstract

We discuss supersymmetric compactifications of heterotic strings in the presence of Hflux and general condensates using the formalism of G-structures and intrinsic torsion. We revisit the examples based on nearly-Kähler coset spaces and show that supersymmetric solutions, where the Bianchi identity is satisfied, can be obtained when both gaugino and dilatino condensates are present.1 Originally, gaugino condensation had been suggested as a supersymmetry breaking mechanism in a Calabi-Yau compactification [4,5]. Here, instead, we consider supersymmetric solutions on manifolds that are not Calabi-Yau.2 See however refs. [23,24] where condensation of fermions in the gravity sector is considered in a different context and ref.[25] which discusses a similar effect in a 5-brane background. Moreover, ref.[26] considered Minkowski vacua in 11-dimensional supergravity with gravitino condensates.

New string vacua from twistor spaces

“…These examples also illustrate a limitation inherent to the usual approach of finding 1 Nearly Kähler manifolds have also appeared in heterotic string theory [18,19]. 2 For the vacua in [16,17], some of which are a special case of those presented here, an effective theory with N = 2 supersymmetry was recently proposed in [20].…”

Gaugino condensation and the cosmological constant

“…Most likely, the heterotic duals of IIB flux backgrounds contain large curvatures, and so lie outside the regime of this analysis. 9 It should be possible solve the undeformed Bianchi identity if we allow more exotic phenomena, specifically dilatino condensation [35].…”

On the consistency of coset space dimensional reduction

“…In the CSDR one allows a generalized invariance condition 16) with W I being a gauge transformation parameter associated to the Killing vector X I . The invariance condition for the reduction of the metric is the same as in the group manifold case since the metric is gauge singlet.…”

“…Let us finally mention that a first step towards embedding the CSDR in string theory was taken in ref. [16] where it was shown that six-dimensional nearly-Kähler coset spaces provide internal spaces 1 A nice review of these developments can be found in ref. [7].…”