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 present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N = 4 and N = 2 gauge theories with adjoint and fundamental matter.

We study a system of fractional D3 and D(-1) branes in a Ramond-Ramond closed string background and show that it describes the gauge instantons of N = 2 super Yang-Mills theory and their interactions with the graviphoton of N = 2 supergravity. In particular, we analyze the instanton moduli space using string theory methods and compute the prepotential of the effective gauge theory exploiting the localization methods of the instanton calculus showing that this leads to the same information given by the topological string. We also comment on the relation between our approach and the so-called Ω-background.

The EGRET telescope has identified a gamma-ray source at the Galactic center. We point out here that the spectral features of this source are compatible with the gamma-ray flux induced by pair annihilations of dark matter weakly interacting massive particles (WIMPs). We show that the discrimination between this interpretation and other viable explanations will be possible with GLAST, the next major gamma-ray telescope in space, on the basis of both the spectral and the angular signature of the WIMP-induced component. If, on the other hand, the data will point to an alternative explanation, we prove that there will still be the possibility for GLAST to single out a weaker dark matter source at the Galactic center. The potential of GLAST has been explored both in the context of a generic simplified toy-model for WIMP dark matter, and in a more specific setup, the case of dark matter neutralinos in the minimal supergravity framework. In the latter, we find that even in the case of moderate dark matter densities in the Galactic center region, there are portions of the parameter space which will be probed by GLAST.

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We study SYM gauge theories living on ALE spaces. Using localization formulae we compute the prepotential (and its gravitational corrections) for SU(N) supersymmetric N = 2, 2 * gauge theories on ALE spaces of the A n type. Furthermore we derive the Poincaré polynomial describing the homologies of the corresponding moduli spaces of self-dual gauge connections. From these results we extract the N = 4 partition function which is a modular form in agreement with the expectations of SL(2, Z) duality.

The prepotential in N = 2 SUSY Yang-Mills theories enjoys remarkable properties. One of the most interesting is its relation to the coordinate on the quantum moduli space u = Tr ϕ 2 that results into recursion equations for the coefficients of the prepotential due to instantons. In this work we show, with an explicit multi-instanton computation, that this relation holds true at arbitrary winding numbers. Even more interestingly we show that its validity extends to the case in which gravitational corrections are taken into account if the correlators are suitably modified. These results apply also to the cases in which matter in the fundamental and in the adjoint is included. We also check that the expressions we find satisfy the chiral ring relations for the gauge case and compute the first gravitational correction.

We study the dynamics of a N = 2 supersymmetric SU (N ) gauge theory with fundamental or adjoint matter in presence of a non trivial Ω-background along a two dimensional plane. The prepotential and chiral correlators of the gauge theory can be obtained, via a saddle point analysis, from an equation which can be viewed as a non commutative version of the "standard" Seiberg and Witten curve.