Strings as Sigma Models and in the Tensionless Limit
This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models with extended supersymmetry. First, the tensionless limit is used to find a IIB supergravity background generated by a tensionless string. The background has the characteristics of a gravitational shock-wave. Then, the quantization of the tensionless string in a pp-wave background is performed and the result is found to agree with what is obtained by taking a tensionless limit directly in the quantized theory of the tensile string. Hence, in the pp-wave background the tensionless limit commutes with quantization. Next, supersymmetric sigma models and the relation between extended world-sheet supersymmetry and target space geometry is studied. The sigma model with N=(2,2) extended supersymmetry is considered and the requirement on the target space to have a bi-Hermitean geometry is reviewed. The Hamiltonian formulation of the model is constructed and the target space is shown to have generalized Kähler geometry. The equivalence between bi-Hermitean geometry and generalized Kähler follows, in this context, from the equivalence between the Lagrangian- and Hamiltonian formulation of the sigma model. Then, T-duality in the Hamiltonian formulation of the sigma model is studied and the explicit T-duality transformation is constructed. It is shown that the transformation is a symplectomorphism, i.e. a generalization of a canonical transformation. Under certain assumptions, the amount of extended supersymmetry present in the sigma model is shown to be preserved under the T-duality transformation. Next, extended supersymmetry in a first order formulation of the sigma model is studied. By requiring N=(2,2) extended world-sheet supersymmetry an intriguing geometrical structure arises and in a special case generalized complex geometry is found to be contained in the new framework.
Source Type:Doctoral Dissertation
Keywords:Theoretical physics; Theoretical Physics; String Theory; Tensionless Strings; Supergravity Backgrounds; Plane Wave; Extended Supersymmetry; Non-Linear Sigma Models; Generalized Complex Geometry; T-duality; Teoretisk fysik
Date of Publication:01/01/2007