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

TL;DR

This paper explores the symmetries of extremal black holes in supergravity, revealing a connection between conformal mechanics, $w_{ abla}$ algebras, and the $AdS_2/CFT_1$ correspondence, with implications for black hole microstates.

Contribution

It demonstrates how the Virasoro symmetry extends to a $w_{ abla}$ algebra in black hole near-horizon dynamics and constructs superconformal mechanics invariant under superextensions of $w_{ abla}$.

Findings

Virasoro symmetry extends to $w_{ abla}$ algebra in black hole backgrounds.

Explicit realization of $AdS_2/CFT_1$ correspondence through phase space diffeomorphisms.

Central charge computed from dimensionally reduced action.

Abstract

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 $w_{\infty}$.