Integrability and Hamiltonian methods in string theory

This thesis consists of two parts. First, we study various aspects of integrability in string theory and in the corresponding two-dimensional effective theories. We begin by reviewing the construction of an effective string action. Then we consider the dimensional reduction of this theory to two dimensions, and determine the Lax pair for the system that leads to integrability. Next, we explore the solution-generating method by constructing the monodromy matrix and by presenting explicit forms of this for systems such as colliding gravitational waves, black holes and other interesting models. We use these insights to apply similar methods to study integrability of the full superstring on the AdS5 x S5 background. We determine a new flat current solution that has a manifest Zinfinity4 automorphism crucial for the construction of the monodromy matrix of the system. Moreover, we perform a Hamiltonian analysis of the full theory, find all the constraints and determine the Poisson brackets between the flat currents. We discuss some important properties of this construction, and outline difficulties associated with the presence of the so-called Schwinger terms. To be able to proceed with the quantization of the system, we next consider gauge fixing of the theory by going to the light-cone gauge and fixing the local fermionic symmetry (kappa-symmetry). This allows us to derive the Dirac brackets between the flat currents. We comment on a possible resolution of the ambiguities in the algebra due to the presence of Schwinger terms.; In the second part of the thesis, we study noncommutativity properties of the boundary string coordinates. In particular, we consider the dynamics of an open membrane with cylindrical topology, in the background of a constant three-form, whose boundary is attached to p-branes. The constrained Hamiltonian formalism is used to determine the noncommutativity of coordinates. The chain of constraints is shown to terminate with a suitable choice of gauge, unlike in the case of the static gauge, where there is an infinite sequence of constraints. This is a new feature that is obtained using an equivalent membrane action due to Bergshoeff, London and Townsend.