We study the D3/D(−1) brane system and show how to compute instanton corrections to correlation functions of gauge theories in four dimensions using open string techniques. In particular we show that the disks with mixed boundary conditions that are typical of the D3/D(−1) system are the sources for the classical instanton solution. This can then be recovered from simple calculations of open string scattering amplitudes in the presence of D-instantons. Exploiting this fact we also relate this stringy description to the standard instanton calculus of field theory.

We show that the boundary state description of a Dp-brane is strictly related to the corresponding classical solution of the low-energy string effective action. By projecting the boundary state on the massless states of the closed string we obtain the tension, the R-R charge and the large distance behavior of the classical solution. We discuss both the case of a single D-brane and that of bound states of two D-branes. We also show that in the R-R sector the boundary state, written in a picture which treats asymmetrically the left and right components, directly yields the R-R gauge potentials.

We study the classical geometry associated to fractional D3-branes of type IIB string theory on IR 4 /Z 2 which provide the gravitational dual for N = 2 super Yang-Mills theory in four dimensions. As one can expect from the lack of conformal invariance on the gauge theory side, the gravitational background displays a repulson-like singularity. It turns out however, that such singularity can be excised by an enhançon mechanism. The complete knowledge of the classical supergravity solution allows us to identify the coupling constant of the dual gauge theory in terms of the string parameters and to find a logarithmic running that is governed precisely by the β function of the N = 2 super Yang-Mills theory. 1 Work partially supported by the European Commission RTN programme HPRN-CT-2000-00131 and by MURST.Contents 1 Introduction 1 2 The geometry of fractional D3-branes 2 3 The enhançon and the dual gauge theory 10

Using the boundary state formalism, we perform a microscopic string analysis of the interaction between two D-branes and provide a local interpretation for the R-R force in the D0-D8 brane system. To do so, we construct BRST invariant vertex operators for the massless R-R states in the asymmetric picture that are proportional to potentials rather than field strengths. The Hilbert space of such R-R states contains combinations of two vectors that decouple from all physical amplitudes, even in the presence of boundaries. Identifying these vectors, we remove the null states and recover duality relations among R-R potentials. If we specify to the D0-D8 brane system, this mechanism implies that the R-R 1-form state has a non-zero overlap with both the D0-brane and the D8-brane, thus explaining from a local point of view the non-vanishing R-R contribution in the interaction for the D0-D8 brane system and those related to it by duality.