We develop and study a D-brane realization of 4D N=2 super Yang-Mills theory. It is a type IIB string theory compactified on R^6\times K3 and containing parallel 7-branes. It can also be regarded as a subsector of Vafa's F-theory compactified on K3\times K3 and is thus dual to the heterotic string on K3\times T^2. We show that the one-loop prepotential in this gauge theory is exactly equal to the interaction produced by classical closed string exchange. A monopole configuration corresponds to an open Dirichlet 5-brane wrapping around $K3$ with ends attached to two 7-branes.
Dirichlet-branes have emerged as important objects in studying nonperturbative string theory. It is important to generalize these objects to more general backgrounds other than the usual flat background. The simplest case is the linear dilaton condensate. The usual Dirichlet boundary condition violates conformal invariance in such a background. We show that by switching on a certain boundary interaction, conformal invariance is restored. An immediate application of this result is to two dimensional string theory.
Polchinski's recent construction of Dirichlet-branes of R-R charges, together with Witten's mechanism for forming bound states of both NS-NS charges and R-R charges, provides a rigorous method to treat these dy-branes. We construct the massless sector of boundary states of D-branes, as well as of dy-strings of charges (p,1). As a consequence, the string tension formula predicted by duality in the type IIB theory is obtained.
An one dimensional supersymmetric matrix model is obtained by quenching the 2D SYM. This model will likely be solved in the large N limit. We also propose an extended supersymmetric matrix model where large N solution can be readily obtained.
With Antal Jevicki and Tamiaki Yoneya, we discuss the origin of the leg factor in 2D string theory. Longitudinal oscillating modes are shown to be responsible for the doubling of time delay in scattering off the Liouville wall. We are planning to study related issues in the black hole background. Better understanding of these stringy phenomena will ultimately lead us to a better understanding of a fundamental formulation of string theory.
We study loop equations in this theory. With an assumption, these equations are solved in the large N limit. This paper is meant to initiate a program of studying the super-gauge theory. We are currently studying other aspects of this theory. Generalization to higher dimensional models is also under consideration.
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li@het.brown.edu