Instanton Calculus and SUSY Gauge Theories on ALE Manifolds

In this contribution we describe how to obtain instanton effects in four dimensional gauge theories by computing string scattering amplitudes in D3/D(-1) brane systems. In particular we study a system of fractional D3/D(-1) branes in a Z_2 orbifold and 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. Using string theory methods we compute the prepoten...

In this paper we explicitly calculate the analogue of the 't Hooft SU(2) Yang--Mills instantons on Gibbons--Hawking multi-centered gravitational instantons which come in two parallel families: the multi-Eguchi--Hanson, or A_k ALE gravitational instantons and the multi-Taub--NUT, or A_k ALF gravitational instantons. We calculate their action and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explic...

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 in...

We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N=2 supersymmetric Yang-Mills theory with gauge group SU(2) compactified on R^3 x S^1. The results are in precise agreement with the semiclassical expansion of the exact metric recently conjectured by Gaiotto, Moore and Neitzke based on considerations related to wall-crossing in the corresponding four-dimensional theory.

The non-perturbative behavior of the N=2 supersymmetric Yang-Mills theories is both highly non-trivial and tractable. In the last three years the valuable progress was achieved in the instanton counting, the direct evaluation of the low-energy effective Wilsonian action of the theory. The localization technique together with the Lorentz deformation of the action provides an elegant way to reduce functional integrals, representing the effective action, to some finite dimension...

We study the instanton contributions of N=2 supersymmetric gauge theory and propose that the instanton moduli space is mapped to the moduli space of punctured spheres. Due to the recursive structure of the boundary in the Deligne-Knudsen-Mumford stable compactification, this leads to a new recursion relation for the instanton coefficients, which is bilinear. Instanton contributions are expressed as integrals on M_{0,n} in the framework of the Liouville F-models. This also sug...

The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theory may be viewed as a prediction for the infinite family of constants F_n measuring the n-instanton contribution to the prepotential F. Here we examine the instanton physics directly, in particular the contribution of the general self-dual solution of topological charge n constructed by Atiyah, Drinfeld, Hitchin and Manin (ADHM). In both the bosonic and supersymmetric cases, we determine both the large- and sho...

We show that the classical equations of motion of the low-energy effective field theory describing the massless modes of the heterotic (or type I) string admit two classes of supersymmetric self--dual backgrounds. The first class, which was already considered in the literature, consists of solutions with a (conformally) flat metric coupled to axionic instantons. The second includes Asymptotically Locally Euclidean (ALE) gravitational instantonic backgrounds coupled to gauge i...

Using standard field theory techniques we compute perturbative and instanton contributions to the Coulomb branch of three-dimensional supersymmetric QCD with N=2 and N=4 supersymmetry and gauge group SU(2). For the N=4 theory with one massless flavor, we confirm the proposal of Seiberg and Witten that the Coulomb branch is the double-cover of the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin. Introducing a hypermultiplet mass term, we show that ...

A self-consistent ansatz is presented for a four-dimensional euclidean solution (instanton) in the vacuum sector of constrained SU(2) Yang-Mills-Higgs theory.