# Heterotic Hyper-Kahler Flux Backgrounds

## TL;DR

This paper constructs exact solutions in heterotic supergravity on Hyper-Kahler manifolds with fluxes, revealing conditions for regularity and the role of brane densities in complex geometries.

## Contribution

It provides new explicit solutions for heterotic flux backgrounds on multi-centered Hyper-Kahler spaces, including Atiyah-Hitchin, with detailed regularity conditions.

## Key findings

- Exact solutions for Gibbons-Hawking and Atiyah-Hitchin spaces.
- Regularity conditions relate circle size at infinity to instanton number.
- Possible smeared five-brane configurations at the bolt.

## Abstract

We study Heterotic supergravity on Hyper-Kahler manifolds in the presence of non-trivial warping and three form flux with Abelian bundles in the large charge limit. We find exact, regular solutions for multi-centered Gibbons-Hawking spaces and Atiyah-Hitchin manifolds. In the case of Atiyah-Hitchin, regularity requires that the circle at infinity is of the same order as the instanton number, which is taken to be large. Alternatively there may be a non-trivial density of smeared five branes at the bolt.