ALE instantons in string effective theory

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 instantons through the so-called ''standard embedding''. We show that some elements of these two classes of solutions are dual to each other in the sense of Buscher's duality. We give a world-sheet interpretation of the heterotic ALE istanton solutions in terms of superconformal N=(4, 4) sigma-models and argue for their validity to all orders in alpha'. Specializing the gravitational background to the Eguchi-Hanson instanton, we compute the indices of the fermionic operators and give the explicit form of all the relevant fermionic and bosonic zero-modes.