Narrow Results

We present a class of extensions of the MSSM characterized by a fully chiral field content (no μ-terms) and no baryon or lepton number violating term in the superpotential due to an extra U′(1) gauge symmetry. The minimal model consists of the usual matter sector with family dependent U′(1) charges, six Higgs weak doublets, and three singlets required to give masses to the Higgsinos and cancel anomalies. We discuss its main features such as the tree level mass spectrum and the constraints on flavor changing processes.

We derive, for N=2 super-Yang-Mills with gauge group SU(2) and massless matter, the supersymmetric quantum mechanical models describing the time evolution of multimonopole configurations in the low energy approximation. This is a first step towards identifying the solitonic states mapped to fundamental excitations by duality in the model with four hypermultiplets in the fundamental representation.

We show how to reduce the non-Abelian Born–Infeld action describing the interaction of two D-particles to the sum of elliptic integrals depending on simple kinematic invariants. This representation gives explicitly all α′ corrections to D-particle dynamics. The α′ corrections induce a stabilization of the classical trajectories such as the "eikonal" which are unstable within the Yang–Mills approximation.

We give an introduction to the recently-established connection between supersymmetric gauge theories and matrix models. We begin by reviewing previous material that is required in order to follow the latest developments. This includes the superfield formulation of gauge theories, holomorphy, the chiral ring, the Konishi anomaly and the large N limit. We then present both the diagrammatic proof of the connection and the one based on the anomaly. Our discussion is entirely field theoretical and self contained.

We study the low energy effective theory describing the dynamics of D-particles. This corresponds to the quantum-mechanical system obtained by dimensional reduction of (9+1)-dimensional supersymmetric Yang-Mills theory to 0+1 dimensions and can be interpreted as the nonrelativistic limit of the Born-Infeld action. We study the system of two like-charged D-particles and find evidence for the existence of non-BPS states whose mass grows like λ^1/3 over the BPS mass. We give a string interpretation of this phenomenon in terms of a linear potential generated by strings stretching from the two D-particles. Some comments on the possible relations to black hole entropy and elevendimensional supergravity are also given.

We study the dynamics of D-particles (D0-branes) in type I' string theory and of the corresponding states in the dual heterotic description. We account for the presence of the two eight-orientifolds (eight-dimensional orientifold planes) and sixteen D8-branes by deriving the appropriate quantum mechanical system. We recover the familiar condition of eight D8-branes for each eight-orientifold. We investigate bound states and compute the phase shifts for the scattering of such states and find that they agree with the expectations from the supergravity action. In the type I' regime we study the motion transverse to the eight-orientifold and find an interesting cancellation effect.