On Heterotic Vacua with Fermionic Expectation Values

Abstract

We study heterotic backgrounds with non-trivial $H$-flux and non-vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge-invariant three-form bilinear ${\Sigma }_{MNP}=\mathrm{tr}\bar{\chi }{\Gamma }_{MNP}\chi$. For Calabi-Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three-form ${\Sigma }_{mnp}$ that must be a singlet of the holonomy group. This condition does not hold anymore when an internal $H$-flux is turned on and $\mathcal{O}({\alpha }^{\prime })$ effects are included. In this paper we study flux compactifications to three and four-dimensions on $G$-structure manifolds. We derive the generic conditions for supersymmetric solutions. We use integrability conditions and Lichnerowicz type arguments to derive a set of constraints whose solution, together with supersymmetry, is sufficient for finding backgrounds with gaugino condensate.

44 pages, minor corrections, references added

References in corpus (8)

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• Explicit Soft Supersymmetry Breaking in the Heterotic M-Theory $B-L$ MSSM
• Consistent truncation with dilatino condensation on nearly Kähler and Calabi-Yau manifolds
• FIMP Dark Matter in Heterotic M-Theory