The Neveu-Schwarz five-brane and its dual geometries

In this paper we discuss two aspects of duality transformations on theNeveu-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 toits CGHS limit, a two-dimensional black hole times $S^3\times T^5$; anintermediate step is provided by the near horizon geometry which is given bythe three-dimensional $BTZ_3$ black hole (being closely related to $AdS_3$)times $S^3\times T^4$. In the second part of the paper we discuss the T-dualitybetween $k$ NS 5-branes and the Taub-NUT spaces respectively ALE spaces, whichare related to the resolution of the $A_{k-1}$ singularities of the non-compactorbifold ${\bf C}^2/{\bf Z}_{k}$. In particular in the framework of N=1supersymmetric gauge theories related to brane box constructions we give themetric dual to two sets of intersecting NS 5-branes. In this way we get apicture of a dual orbifold background ${\bf C}^3/ \Gamma$ which is fiberedtogether out of two N=2 models ($\Gamma={\bf Z}_k\times {\bf Z}_{k'}$). Finallywe also discuss the intersection of NS 5-branes with D branes, which can serveas probes of the dual background spaces.Comment: 18pp, added reference