Moduli in general SU(3)-structure heterotic compactifications

In this thesis, we study compactifiations of ten-dimensional heterotic supergravity at O(α'), focusing on the moduli of such compactifications. We begin by studying supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The compactifications are of the form M10 = M4 x X, where M4 is four-dimensional Minkowski space, and X is a six-dimensional manifold of what we refer to as heterotic SU(3)-structure. We show that this system can be put in terms of a holomorphic operator D on a bundle Q = T* X ⊕ End(TX) ⊕ End(V ) ⊕ TX, defined by a series of extensions. Here V is the E8 x E8 gauge-bundle, and TX is the tangent bundle of the compact space X. We proceed to compute the infinitesimal deformation space of this structure, given by TM = H(0,1)(Q), which constitutes the infinitesimal spectrum of the lower energy four-dimensional theory. In doing so, we find an over counting of moduli by H(0,1)(End(TX)), which can be reinterpreted as O(α') field redefinitions. In the next part of the thesis, we consider non-maximally symmetric compactifications of the form M10 = M3 x Y , where M3 is three-dimensional Minkowski space, and Y is a seven-dimensional non-compact manifold with a G2-structure. We write X → Y → ℝ, where X is a six dimensional compact space of half- at SU(3)-structure, non-trivially fibered over ℝ. These compactifications are known as domain wall compactifications. By focusing on coset compactifications, we show that the compact space X can be endowed with non-trivial torsion, which can be used in a combination with %alpha;'-effects to stabilise all geometric moduli. The domain wall can further be lifted to a maximally symmetric AdS vacuum by inclusion of non-perturbative effects in a heterotic KKLT scenario. Finally, we consider domain wall compactifications where X is a Calabi-Yau. We show that by considering such compactifications, one can evade the usual no-go theorems for flux in Calabi-Yau compactifications, allowing flux to be used as a tool in such compactifications, even when X is Kähler. The ultimate success of these compactifications depends on the possibility of lifting such vacua to maximally symmetric ones by means of e.g. non-perturbative effects.