Abstract
Recently an exact worldsheet description of strings propagating in certain black hole microstate geometries was constructed in terms of null-gauged WZW models. In this paper we consider a family of such coset models, in which the currents being gauged are specified by a set of parameters that a priori take arbitrary values. We show that consistency of the spectrum of the worldsheet CFT implies a set of quantisation conditions and parity restrictions on the gauging parameters. We also derive these constraints from an independent geometrical analysis of smoothness, absence of horizons and absence of closed timelike curves. This allows us to prove that the complete set of consistent backgrounds in this class of models is precisely the general family of (NS5-decoupled) non-BPS solutions known as the JMaRT solutions, together with their various (BPS and non-BPS) limits. We clarify several aspects of these backgrounds by expressing their six-dimensional solutions explicitly in terms of five non-negative integers and a single length-scale. Finally we study non-trivial two-charge limits, and exhibit a novel set of non-BPS supergravity solutions describing bound states of NS5 branes carrying momentum charge.
Highlights
In which to study black hole microstates in string theory
Recently an exact worldsheet description of strings propagating in certain black hole microstate geometries was constructed in terms of null-gauged WZW models
Configurations that have come to be known as circular supertubes [2, 3] were important early supergravity solutions describing specific microstates of the two-charge system, in particular in the D1-D5 or NS5-F1 duality frames
Summary
We review some relevant aspects of the models that we shall study in this work. Since the Cartan direction in SL(2, R) is timelike, and that of SU(2) is spacelike, and the levels are the same, one can form null linear combinations Js3l ± Js3u in both holomorphic and antiholomorphic sectors of the worldsheet theory. Gauging such null currents leads [36] to the background sourced by a circular array of NS5 branes on their Coulomb branch [41,42,43]. We review the basics of these constructions and consider the most general pair of such chiral null currents that can be gauged. We derive the corresponding supergravity fields, written as functions of the general gauging parameters
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