Title:

Duality and geometry of string theory

String theory possesses duality symmetries that relate different string backgrounds. One symmetry is known as Tduality symmetry. In general, when n dimensions are toroidally compactified, the Tduality group is O(n, n, Z). String theory has another duality symmetry known as Sduality, which does not commute with Tduality. The full Sduality group is SL(2,Z). The last duality symmetry is Uduality symmetry, which is En(Z) for type II string theory on an ntorus. Duality symmetries tell us that strings experience geometry differently from particles. In order to understand string theory, a new way to understand string geometry is required. In this thesis, first we introduce some basic ideas on duality symmetries in string theory, namely, Tduality, Sduality, and Uduality. Next, we review string field theory. We, then, provide the basic constructions of DFT and EFT. Next, we consider the finite gauge transformations of DFT and EFT. The expressions for finite gauge transformations in double field theory with duality group O(n,n) are generalized to give expressions for finite gauge transformations for extended field theories with duality groups SL(5,R), SO(5,5) and E_6. Another topic is the Tduality chain of special holonomy domain wall solutions. This example can arise in string theory in solutions in which these backgrounds appear as fibres over a line. The cases with 3torus with Hflux over a line were obtained from identifications of suitable NS5brane solutions, and are dual to D8brane solutions. This Tduality chain implies that K3 should have a limit in which it degenerates to a long neck capped off by suitable smooth geometries. A similar result applies for the higher dimensional analogues of the nilfold. In each case, the space admits a multidomain wall type metric that has special holonomy, so that taking the product of the domain wall solution with Minkowski space gives a supersymmetric solution.
