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 normalΣMNP= tr χ¯normalΓMNPχ. For Calabi‐Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three‐form Σmnp that must be a singlet of the holonomy group. This condition does not hold anymore when an internal H‐flux is turned on and O(α′) 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.

The Infinitesimal Moduli Space of Heterotic G 2 Systems

“…One can define a canonical differential complex Λ * (Y ) as a sub complex of the de Rham complex [32], and the associated cohomologies Ȟ * (Y ) have similarities with the Dolbeault complex of complex geometry. Heterotic vacua on seven dimensional non-compact manifolds with an integrable G 2 structure lead to fourdimensional domain wall solution that are of interest in physics [33][34][35][36][37][38][39][40][41][42][43][44][45][46], and whose moduli determine the massless sector of the four-dimensional theory. Furthermore, families of SU (3) structure manifolds can be studied through an embedding in integrable G 2 geometry.…”

$$ \mathcal{N} $$ = 1 supersymmetric Double Field Theory and the generalized Kerr-Schild ansatz

“…a phenomenological scenario the most interesting fermionic contributions are related with gaugino condensation [36][37][38]. For this reason it is enough to imposeΘ a = 0.…”

Moduli and Hidden Matter in Heterotic M-Theory with an Anomalous $U(1)$ Hidden Sector

“…In [36], we analyzed a possible SUSY-breaking mechanism for the vacua found in [26], namely gaugino condensation in the hidden sector. The condensate induces non-zero F-terms in the 4D effective theory which break SUSY globally [37][38][39][40][41][42][43][44][45][46][47]. This effect is mediated by gravity and induces calculable moduli-dependent soft SUSY-breaking terms in the observable sector.…”