The Neveu-Schwarz Five-Brane and its Dual Geometries

TL;DR

This paper explores duality transformations of NS 5-brane solutions in string theories, revealing connections to black hole geometries, orbifolds, and intersecting brane configurations, advancing understanding of string dualities and geometric backgrounds.

Contribution

It demonstrates the U-duality between non-extremal NS 5-branes and CGHS black holes, and analyzes T-duality relating NS 5-branes to Taub-NUT and ALE spaces, providing new dual geometric descriptions.

Findings

U-dual of NS 5-brane is a 2D black hole times spheres and tori.

T-duality relates NS 5-branes to Taub-NUT and ALE spaces.

Constructs dual orbifold backgrounds from intersecting NS 5-branes.

Abstract

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 $S^3\times T^5$; 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 $S^3\times T^4$. 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 ${\bf C}^2/{\bf Z}_{k}$. 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 ${\bf C}^3/ \Gamma$ which is fibered together out of two N=2 models ($\Gamma={\bf Z}_k\times {\bf Z}_{k'}$). Finally we also discuss the intersection of NS 5-branes with D branes, which can serve as probes of the dual background spaces.