Some Applications of Hyperbolic Geometry in String Perturbation Theory
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Date
2019-08-19
Authors
Moosavian, Seyed Faroogh
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
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 can
be achieved using the hyperbolic parameters. The decomposition is appropriate to define
off-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 local
coordinates around the punctures, we associate local coordinates around the punctures in
various regions of the moduli space. The next ingredient to define the off-shell amplitudes
is to provide a method to integrate the off-shell string measure over the moduli space of
hyperbolic 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-changing
operators. We provide such a distribution. Finally, we illustrate the whole construction in
few examples. We then describe the construction of a consistent string field theory using
the tools from hyperbolic geometry.
Description
Keywords
off-shell amplitudes, string perturbation theory, string field theory