New half supersymmetric solutions of the heterotic string

Understand

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.