Instanton Effects in Supersymmetric Yang-Mills Theories on ALE Gravitational Backgrounds

Abstract

In this letter we report on the computation of instanton-dominated correlation functions in supersymmetric Yang-Mills theories on Asymptotically Locally Euclidean spaces. Following the approach of Kronheimer and Nakajima, we explicitly construct the self-dual connection on Asymptotically Locally Euclidean spaces necessary to perform such computations. We restrict our attention to the simplest case of an SU(2) connection with lowest Chern class on the Eguchi-Hanson gravitational background. ⋆ Work partially supported by E.C. Grant CHRX-CT93-0340. Introduction Understanding non-perturbative phenomena is a key issue in any field theory. These effects are supposed to play a fundamental role in the explanation of confinement as well as dynamical supersymmetry (SUSY) breaking and many interesting results that go beyond perturbation theory have been recently obtained for supersymmetric Yang-Mills theory (SYM from now on) on flat [1,2,3] and curved manifolds [4,5]. Constant values for instanton dominated correlation functions may be related to topological invariants of the moduli space of YM connections on the base manifold [6,7]. When clustering applies, they give rise to the formation of chiral condensates. The local extension of the results obtained for globally SYM theories presents formidable difficulties, the main one being the non renormalizability of the resulting quantum (super-)gravity. A way to circumvent this problem is to have the theory embedded in a suitable string theory which will act as a regulator. One thus seems to be lead to consider only the four dimensional effective field theories which emerge as low-energy limits of consistent superstring compactifications. Euclidean supersymmetric solutions of the heterotic (or Type I) string equations of motion can be found setting to zero the fermionic fields together with their SUSY variations. For these solutions not to get corrections in (the σ-model coupling constant) α , one is lead to impose the “standard-embedding” of the generalized spin connection into the gauge group [8,9,10,11,12]. Leaving aside solutions with non-trivial configurations of the scalar fields [13,14,15], which may be related to monopole solutions [16], one has the option of either taking a constant dilaton background [10] or a non-trivial axionic instanton [13,8,9]. In the following we will mainly concentrate on the former choice which leads to self-dual gauge connections on manifolds with self-dual curvature. We further restrict our investigation to self-dual ALE instantons. They have been completely classified by Hitchin and Kronheimer [17,18] and, as shown by Kronheimer and

Cite this paper

@inproceedings{Bianchi1995InstantonEI, title={Instanton Effects in Supersymmetric Yang-Mills Theories on ALE Gravitational Backgrounds}, author={Massimo Bianchi and Francesco Fucito and Giancarlo Rossi and Maurizio Martellini}, year={1995} }