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 X 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 X 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 C-2/Z(k). 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 C-3/Gamma which is fibered together out of two N = 2 models ( = Z(k) X Z(k')). Finally we also discuss the intersection of NS 5-branes with D branes, which can serve as probes of the dual background spaces.