AdS_2/CFT_1, Canonical Transformations and Superconformal Mechanics

TL;DR

This paper introduces a conformal mechanics model equivalent to a charged massive particle near an extremal Reissner-Nordström black hole horizon, utilizing canonical transformations to connect to superconformal mechanics.

Contribution

It presents a simple conformal mechanics model and constructs the Hamiltonian of an N=4 superparticle on AdS_2×S^2 using canonical transformations.

Findings

Model is classically equivalent to particle near black hole horizon

Canonical transformation links mechanics to superconformal structure

Constructed Hamiltonian for N=4 superparticle

Abstract

We propose a simple conformal mechanics model which is classically equivalent to a charged massive particle propagating near the AdS_2\times S^2 horizon of an extreme Reissner-Nordstr\"om black hole. The equivalence holds for any finite value of the black hole mass and with both the radial and angular degrees of freedom of the particle taken into account. It is ensured by the existence of a canonical transformation in the Hamiltonian formalism. Using this transformation, we construct the Hamiltonian of a N=4 superparticle on AdS_2\times S^2 background.