Abstract
We determine a consistent phase space for a theory consisting in the Einstein-Hilbert action coupled to matter fields (dilaton, one-form, two-form) and containing three-dimensional black strings (the Horne-Horowitz solution and generalizations thereof). The theory at hand is the low energy effective action for the bosonic sector of heterotic string theory. We find a consistent set of boundary conditions whose algebra of asymptotic charges consist in a single Virasoro algebra supplemented by three global u(1) generators. We also discuss the thermodynamics of the zero-mode solutions and point out some peculiar features of this system.
Highlights
Constant and suitable boundary conditions admits an action of the two-dimensional conformal group [1], thereby suggesting a quantum description in terms of a two-dimensional CFT
What is lacking in these cases is a clear definition of the corresponding phase space, its symmetries, and whether these are relevant to understand thermal properties of those objects
We present a consistent set of boundary conditions including these solutions and determine its asymptotic symmetry algebra of charges, the detailed derivation of which is relegated to appendices B and C
Summary
The black string geometries we will be considering are the ones described in [40], consisting of a generalization of the Horne-Horowitz black string [34] The latter can be viewed as the target space of a SL(2,R)×R R gauged. The black string of [40] is a generalization obtained with an extra deformation using another available exact current bilinear. As such, these geometries describe exact string theory models. The background fields are a three-dimensional metric, a Kalb-Ramond two-form B, an Abelian electromagnetic gauge potential A, and a dilaton Φ. The charged black string of [40] is an exact background, reached by a double marginal deformation of the SL(2, R) sigma model. The study of the geodesics in the background (A.1) shows that spacelike geodesics end at i0 (for r → ∞, with t and x finite), while null geodesics reach r → ∞ for infinite values of t and x corresponding to I±
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