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 M<sub>10</sub> = M<sub>4</sub> x X, where M<sub>4</sub> 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 E<sub>8</sub> x E<sub>8</sub> 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<sup>(0,1)</sup>(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<sup>(0,1)</sup>(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 M<sub>10</sub> = M<sub>3</sub> x Y , where M<sub>3</sub> is three-dimensional Minkowski space, and Y is a seven-dimensional non-compact manifold with a G<sub>2</sub>-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 %α'-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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:658448 |
| Date | January 2014 |
| Creators | Svanes, Eirik Eik |
| Contributors | Lukas, Andre; de la Ossa, Xenia |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:3c7089a8-1bf0-4f52-87a0-1c64e49874f4 |
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