The Neveu-Schwarz five-brane and its dual geometries

In this paper we discuss two aspects of duality transformations on the Neveu-Schwarz (NS) 5-brane solutions in type II and heterotic string theories. First we demonstrate that the non-extremal NS 5-brane background is U-dual to its CGHS limit, a two-dimensional black hole times S 3×T 5; an intermediate step is provided by the near horizon geometry which is given by the three-dimensional BTZ 3 black hole (being closely related to AdS 3) times S 3×T 4. In the second part of the paper we discuss the T-duality between k NS 5-branes and the Taub-NUT spaces respectively ALE spaces, which are related to the resolution of the A k−1 singularities of the non-compact orbifold C2/Zk. In particular in the framework of N=1 supersymmetric gauge theories related to brane box constructions we give the metric dual to two sets of intersecting NS 5-branes. In this way we get a picture of a dual orbifold background C3/Γ which is fibered together out of two N=2 models (Γ=Zk×Zk′). Finally we also discuss the intersection of NS 5-branes with D branes, which can serve as probes of the dual background spaces.