Abstract
We revisit AdS_4 heterotic compactifications on nearly K\"ahler manifolds in the presence of H-flux and certain fermion condensates. Unlike previous studies, we do not assume the vanishing of the supersymmetry variations. Instead we determine the full equations of motion originating from the ten-dimensional action, and subsequently we provide explicit solutions to them on nearly K\"ahler manifolds at first order in alpha'. The Bianchi identity is also taken into account in order to guarantee the absence of all anomalies. In the presence of H-flux, which is identified with the torsion of the internal space, as well as of fermion condensates in the gaugino and dilatino sectors, new solutions are determined. These solutions provide a full classification of consistent backgrounds of heterotic supergravity under our assumptions. All the new solutions are non-supersymmetric, while previously known supersymmetric ones are recovered too. Our results indicate that fully consistent (supersymmetric or not) heterotic vacua on nearly K\"ahler manifolds are scarce, even on AdS_4, and they can be completely classified.
Highlights
In the present paper we extend the analysis of [9] by implementing dilatino condensates into the theory
Instead we determine the full equations of motion originating from the ten-dimensional action, and subsequently we provide explicit solutions to them on nearly Kahler manifolds at first order in α′
The low-energy field theory limit of heterotic string theory is given by d=10, N =1 supergravity coupled to a super-Yang-Mills multiplet and it is defined on the 10d spacetime M
Summary
The term in the action which is proportional to χγM γABFABγM λ will be ignored in the following This is a legitimate choice once we assume that there is no vacuum expectation value related to bilinears of the mixed form χλ and the like. Corrections, most importantly the gauge sector in the action and the non-trivial corrections in the Bianchi identity In that case it is far from obvious whether the equations of motion follow from the supersymmetry equations and the Bianchi identity [8]. Over the space-time fermionic degrees of freedom At this stage, assumptions about the fermionic quantum correlators enter: we assume the presence of a suitable space-time gaugino condensate as a backdrop for the bosonic equations, namely tr χγ5χ∗ = i Λ3 but tr χM χ = tr χM χ∗ = 0. A certain class of such internal spaces is given by nearly Kahler manifolds, which we study in the present paper
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