New half supersymmetric solutions of the heterotic string

Abstract

We describe all supersymmetric solutions of the heterotic string which preserve 8 supersymmetries and show that are distinguished by the holonomy, hol(∇), of the connection, ∇, with skew-symmetric torsion. The hol(∇) ⊂eq 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, Lie (G)=5,1, sl(2,) su(2) or cw6. 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 Lie (G)=sl(2,) 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 hol(∇) ⊂eq8 solutions are superpositions of fundamental strings and pp-waves in flat space, which may also include a null rotation. The hol(∇)=\1\ heterotic string backgrounds which preserve 8 supersymmetries are Lorentzian group manifolds.