Rennecke, Felix (2014): O(d,d) Targetspace duality in string theory. Dissertation, LMU München: Faculty of Physics 

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Abstract
In this thesis various aspects of targetspace duality in closed bosonic string theory are studied. It begins by introducing generalized geometry as the main mathematical framework. In analogy to general relativity with the Riemannian metric as dynamical quantity, a unified description for string backgrounds – Riemannian metrics together with KalbRamond twoform fields – is approached via Courant algebroids on the generalized tangent bundle equipped with a generalized metric. The dual background configuration, i.e. a metric and a bivector field, is described by the generalized cotangent bundle. The absence of a conventional curvature tensor and consequently the problem of defining generalized gravity theories on Courant algebroids is investigated in detail. This leads to the introduction of Lie algebroids whose differential geometry is suitable for the formulation of gravity theories. Different such theories are shown to be interrelated by appropriate homomorphisms. This proves to be useful for describing nongeometric backgrounds. Targetspace duality is introduced in terms of O(d,d)duality which identifies twodimensional nonlinear sigma models for different string backgrounds as physically equivalent under certain conditions: The backgrounds and coordinates of the dual theories have to be related by certain O(d, d) transformations. In particular, integrability conditions of the dual coordinates are formulated in terms of Courant algebroids. Apart from (nonabelian) Tduality, O(d,d)duality contains the novel Poissonduality induced by Poisson structures. T and Poissonduality are applied to the threetorus with constant Hflux which shows the existence of nongeometric backgrounds. The latter exceed conventional conceptions of geometry as they cannot be described globally. The problem of describing nongeometric backgrounds is approached with generalizes geometry. A unified description of Tdual backgrounds is given in terms of protoLie bialgebroids – one for the geometric sector and another for the nongeometric one. They combine into a Courant algebroid whose anomalous Jacobi identity provides conditions for the concurrent appearance of dual fluxes. The absence of a gravity theory leads to the restriction to Lie algebroids. Their gravity theories allow for a global description of nongeometric backgrounds by an exact prescription for the patching of these backgrounds. The description extends to all possible supergravity theories. The question whether a unified description of dual backgrounds is possible is reconsidered in a manifestly Tduality invariant conformal field theory approach. Dual coordinates are treated on equal footing. Modular invariance of the oneloop partition function together with the premise of physical intermediate states in fourtachyon scattering inevitably leads to the appearance of the strong constraint of double field theory on noncompact spaces. Toroidally compactified directions do not require a constraint. This explains the appearance of the strong constraint and justifies possible attenuations.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  Physik, Stringtheorie, Dualiäten, Generalisierte Geometrie, Konforme Feldtheorie 
Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  9. October 2014 
1. Referee:  Blumenhagen, Ralph 
MD5 Checksum of the PDFfile:  84a81b2c761dfa6b82fa6fa3372c6d73 
Signature of the printed copy:  0001/UMC 22477 
ID Code:  17583 
Deposited On:  10. Nov 2014 10:45 
Last Modified:  20. Jul 2016 10:37 