ALE Instantons in String Effective Theory

TL;DR

This paper explores supersymmetric self-dual backgrounds in heterotic string effective theory, revealing dualities between different instanton solutions and analyzing their world-sheet and zero-mode properties.

Contribution

It identifies two classes of supersymmetric self-dual solutions, establishes dualities between them, and provides a world-sheet interpretation and zero-mode analysis for ALE instantons.

Findings

Two classes of supersymmetric self-dual backgrounds identified.

Duality relations established between different instanton solutions.

Explicit zero-mode spectra computed for Eguchi-Hanson instanton.

Abstract

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 $N=(4,4)$ $\s$--models and argue for their validity to all orders in $\alpha^\prime$. 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.}