On Heterotic Vacua with Fermionic Expectation Values

Ruben Minasian (1) , Michela Petrini (2) , Eirik Eik Svanes (3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
3 Institut Lagrange de Paris

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 $\Sigma_{MNP}={\rm tr}\:\bar\chi\Gamma_{MNP}\chi$. 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 ${\cal O}(\alpha')$ 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.

Keywords: Supersymmetry; Heterotic Supergravity; Gaugino Condensates

Domains: Physics [physics]; General Relativity and Quantum Cosmology [gr-qc]

Ruben Minasian, Michela Petrini, Eirik Eik Svanes. On Heterotic Vacua with Fermionic Expectation Values. Fortschritte der Physik / Progress of Physics, 2017, 65 (3-4), pp.1700010. ⟨10.1002/prop.201700010⟩. ⟨cea-01474713⟩