w_{\infty} Algebras, Conformal Mechanics, and Black Holes

Details w_{\infty} Algebras, Conformal Mechanics, and Black Holes w_{\infty} Algebras, Conformal Mechanics, and Black Holes

1999-10-07

arxiv.org/abs/hep-th/9910065v3

Class.Quant.Grav. 17 (2000) 1731-1748

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 23 pages, minor errors corrected, references added; final version to appear in Class. Quant. Grav

Scientific paper

10.1088/0264-9381/17/8/301

We discuss BPS solitons in gauged ${\cal N}=2$, D=4 supergravity. The solitons represent extremal black holes interpolating between different vacua of anti-de Sitter spaces. The isometry superalgebras are determined and the motion of a superparticle in the extremal black hole background is studied and confronted with superconformal mechanics. We show that the Virasoro symmetry of conformal mechanics, which describes the dynamics of the superparticle near the horizon of the extremal black hole under consideration, extends to a symmetry under the $w_{\infty}$ algebra of area-preserving diffeomorphisms. We find that a Virasoro subalgebra of $w_{\infty}$ can be associated to the Virasoro algebra of the asymptotic symmetries of $AdS_2$. In this way spacetime diffeomorphisms of $AdS_2$ translate into diffeomorphisms in phase space: our system offers an explicit realization of the $AdS_2/CFT_1$ correspondence. Using the dimensionally reduced action, the central charge is computed. Finally, we also present generalizations of superconformal mechanics which are invariant under ${\cal N} =1$ and ${\cal N} =2$ superextensions of $w_{\infty}$.

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