Strings as sigma models and in the tensionless limit

TL;DR

This thesis explores the tensionless limit of strings and supersymmetric sigma models, revealing new geometric structures, background solutions, and properties of T-duality in string theory.

Contribution

It demonstrates the commutation of tensionless limit with quantization, constructs explicit T-duality transformations, and uncovers generalized complex geometry within sigma models.

Findings

Tensionless limit commutes with quantization.

Explicit T-duality as a symplectomorphism.

Generalized complex geometry arises in sigma models.

Abstract

This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models. The tensionless limit is used to find a IIB supergravity background generated by a tensionless string. Quantization of the tensionless string in a pp-wave background is performed and the tensionless limit is found to commute with quantization. Further, the sigma model with N=(2,2) extended world-sheet supersymmetry is considered and the requirement on the target space to have a bi-Hermitean geometry is reviewed. It is shown that the equivalence between bi-Hermitean geometry and generalized Kahler follows, in this context, from the equivalence between the Lagrangian- and Hamiltonian formulation of the model. Moreover, the explicit T-duality transformation in the Hamiltonian formulation of the sigma model is constructed and shown to be a symplectomorphism. Under certain assumptions, the amount of extended supersymmetry present in the sigma model is shown to be preserved under T-duality. Further, by requiring N=(2,2) extended supersymmetry in a first order formulation of the sigma model an intriguing geometrical structure arises and in a special case generalized complex geometry is found to be contained in the new framework.