New half supersymmetric solutions of the heterotic string

TL;DR

This paper classifies all 8-supersymmetry heterotic string solutions based on the holonomy of a torsionful connection, constructing new solutions and analyzing their geometric and physical properties.

Contribution

It provides a complete classification of half-supersymmetric heterotic solutions using holonomy, introduces new solutions with specific Lie algebra structures, and explores their physical interpretations.

Findings

Solutions with holonomy in SU(2) are principal bundles over hyper-Kähler manifolds.

New solutions characterized by three integers with continuous moduli.

Holonomy in R^8 corresponds to superpositions of strings and waves.

Abstract

We describe all supersymmetric solutions of the heterotic string which preserve 8 supersymmetries and show that are distinguished by the holonomy, ${\rm hol}(\hat\nabla)$, of the connection, $\hat\nabla$, with skew-symmetric torsion. The ${\rm hol}(\hat\nabla) \subseteq SU(2)$ solutions are principal bundles over a 4-dimensional hyper-K\"ahler manifold equipped with a anti-self-dual connection and fibre group $G$ which has Lie algebra, ${\mathfrak Lie} (G)=\bR^{5,1}$, $\mathfrak{sl}(2,\bR)\oplus \mathfrak{su}(2)$ or $\mathfrak{cw}_6$. Some of the solutions have the interpretation as 5-branes wrapped on $G$ with transverse space any hyper-K\"ahler 4-dimensional manifold. We construct new solutions for ${\mathfrak Lie} (G)=\mathfrak{sl}(2,\bR)\oplus \mathfrak{su}(2)$ and show that are characterized by 3 integers and have continuous moduli. There is also a smooth family in this class with one asymptotic region and the dilaton is bounded everywhere on the spacetime. We also demonstrate that the worldvolume theory of the backgrounds with holonomy SU(2) can be understood in terms of gauged WZW models for which the gauge fields are composite. The ${\rm hol}(\hat\nabla) \subseteq\bR^8$ solutions are superpositions of fundamental strings and pp-waves in flat space, which may also include a null rotation. The ${\rm hol}(\hat\nabla)=\{1\}$ heterotic string backgrounds which preserve 8 supersymmetries are Lorentzian group manifolds.