Some Applications of Hyperbolic Geometry in String Perturbation Theory

off-shell amplitudes;string perturbation theory;string field theory

Moosavian, Seyed Farooghaffiliation1:Faculty of Science ; advisor:Gaiotto, Davide ; Gaiotto, Davide ;

University of Waterloo

关键词: off-shell amplitudes;    string perturbation theory;    string field theory;    Doctoral Thesis;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/14903/1/Moosavian_SeyedFaroogh.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this thesis, we explore some applications of recent developments in the hyperbolic geometry of Riemann surfaces and moduli spaces thereof in string theory.First we show how a proper decomposition of the moduli space of hyperbolic surfaces canbe achieved using the hyperbolic parameters. The decomposition is appropriate to defineoff-shell amplitudes in bosonic-string, heterotic-string and type-II superstring theories.Since the off-shell amplitudes in bosonic-string theory are dependent on the choice of localcoordinates around the punctures, we associate local coordinates around the punctures invarious regions of the moduli space. The next ingredient to define the off-shell amplitudesis to provide a method to integrate the off-shell string measure over the moduli space ofhyperbolic surfaces. We next show how the integrals appearing in the definition of bosonic-string, heterotic-string and type-II superstring amplitudes can be computed by lifting them to appropriate covering spaces of the moduli space. In heterotic-string and typeII superstring theories, we also need to provide a proper distribution of picture-changingoperators. We provide such a distribution. Finally, we illustrate the whole construction infew examples. We then describe the construction of a consistent string field theory usingthe tools from hyperbolic geometry.