Symmetries and interactions in matrix string theory

This PhD-thesis reviews matrix string theory and recent developments therein. Emphasis is put on symmetries, interactions and scattering processes in the matrix model. We start with an introduction to matrix string theory and a review of the orbifold model that flows out of matrix string theory in the strong YM coupling limit. Then we turn our attention to the appearance of U-duality symmetry in gauge models, after a (very) short summary of string duality, D-branes and M-theory. The last chapter reviews matrix string interactions and scattering processes in the high energy limit. Also, pair production of D-particles is studied in detail. D-pair production is expected to give important corrections to high energy scattering processes in string theory.Comment: 115 pages, PhD-thesis defended at the University of Amsterdam, september 1999. Hardcopies available via the autho

Duality symmetry of N=4 Yang-Mills theory on T^3

We study the spectrum of BPS states in N=4 supersymmetric U(N) Yang-Mills theory. This theory has been proposed to describe M-theory on T^3 in the discrete light-cone formalism. We find that the degeneracy of irreducible BPS bound states in this model exhibits a (partially hidden) SL(5,Z) duality symmetry. Besides the electro-magnetic symmetry, this duality group also contains Nahm-like transformations that interchange the rank N of the gauge group with some of the magnetic or electric fluxes. In the M-theory interpretation, this mapping amounts to a reflection that interchanges the longitudinal direction with one of the transverse directions.Comment: 16 pages, Latex, no figures. Some eqns in section 4 on Nahm duality correcte

High Energy Scattering and D-Pair Creation in Matrix String Theory

In this paper we use the matrix string approach to begin a study of high energy scattering processes in M-theory. In particular we exhibit an instanton-type configuration in 1+1 super-Yang-Mills theory that can be interpreted as a non-perturbative description of a string interaction. This solution is used to describe high energy processes with non-zero longitudinal momentum exchange, in which an arbitrary number of eigenvalues get transferred between the two scattering states. We describe a direct correspondence between these semi-classical SYM configurations and the Gross-Mende saddle points. We also study in detail the pair production of D-particles via a one-loop calculation which in the 1+1D gauge theory language is described by the (perturbative) transition between states with different electric flux. Finally, we discuss a possible connection between these calculations in which D-particle production gives important corrections to the Gross-Mende process.Comment: 44 pages, harvmac; minor reference and equation correction