Gravitational Instantons in Heterotic String Theory: The H-Map and the Moduli Deformations of (4,4) Superconformal Field Theories

TL;DR

This paper explores string propagation in heterotic instanton backgrounds, introducing generalized HyperKähler manifolds, a universal SU(6) symmetry via the h-map, and analyzing moduli deformations within a 16-dimensional space.

Contribution

It defines generalized HyperKähler manifolds, proposes a universal h-map construction, and analyzes moduli deformations of (4,4) superconformal theories in heterotic string backgrounds.

Findings

Universal SU(6) symmetry predicted for string modes

Deformations of the SU(2) X R instanton identified

16-dimensional moduli space characterized for certain backgrounds

Abstract

We study the problem of string propagation in a general instanton background for the case of the complete heterotic superstring. We define the concept of generalized HyperK\" ahler manifolds and we relate it to (4,4) superconformal theories. We propose a generalized h-map construction that predicts a universal SU(6) symmetry for the modes of the string excitations moving in an instanton background. We also discuss the role of abstract $N$=4 moduli and, applying it to the particular limit case of the solvable SU(2) X R instanton found by Callan et al. we show that it admits deformations and corresponds to a point in a 16-dimensional moduli space. The geometrical characterization of the other spaces in the same moduli-space remains an outstanding problem.