Jeschek, Claus (2005): Background geometries in string and Mtheory. Dissertation, LMU München: Faculty of Physics 

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Abstract
In this thesis we consider background geometries resulting from string theory compactifications. In particular, we investigate supersymmetric vacuum spaces of supergravity theories and topological twisted sigma models by means of classical and generalised Gstructures. In the first part we compactify 11d supergravity on sevendimensional manifolds due to phenomenological reasons. A certain amount of supersymmetry forces the internal background to admit a classical SU(3) or G2structure. Especially, in the case that the fourdimensional space is maximally symmetric and four form fluxes are present we calculate the relation to the intrinsic torsion. The second and main part is twofold. Firstly, we realise that generalised geometries on sixdimensional manifolds are a natural framework to study Tduality and mirror symmetry, in particular if the Bfield is nonvanishing. An explicit mirror map is given and we apply this idea to the generalised formulation of a topological twisted sigma model. Implications of mirror symmetry are studied, e.g. observables and topological A and Bbranes. Secondly, we show that sevendimensional NSNS backgrounds in type II supergravity theories can be described by generalised G2geometries. A compactification on six manifolds leads to a new structure. We call this geometry a generalised SU(3)structure. We study the relation between generalised SU(3) and G2structures on six and sevenmanifolds and generalise the Hitchinflow equations. Finally, we further develop the generalised SU(3) and G2structures via a constrained variational principle to incorporate also the remaining physical RR fields.
Item Type:  Thesis (Dissertation, LMU Munich) 

Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  13. December 2005 
1. Referee:  Lüst, Dieter 
Persistent Identifier (URN):  urn:nbn:de:bvb:1946722 
MD5 Checksum of the PDFfile:  be9288370b5a745f4fd3e7820d62a4bf 
Signature of the printed copy:  0001/UMC 15043 
ID Code:  4672 
Deposited On:  29. Dec 2005 
Last Modified:  16. Oct 2012 07:54 