(Generalized) Conformal Quantum Mechanics of 0-Branes and Two-Dimensional Dilaton Gravity

TL;DR

This paper explores the connection between conformal quantum mechanics of 0-branes and two-dimensional dilaton gravity, revealing how different brane actions relate to known gravity models and their symmetries.

Contribution

It establishes a link between 0-brane quantum mechanics and 2D dilaton gravity models, clarifying their symmetry properties and conformal structures.

Findings

Non-dilatonic 0-brane leads to a conformal Liouville theory.

Dilatonic 0-brane results in a non-conformal 2D gravity model.

SL(2,R) symmetry is realized in the associated 2D models.

Abstract

We study the relation between the (generalized) conformal quantum mechanics of 0-branes and the two-dimensional dilaton gravity. The two-dimensional actions obtained from the supergravity effective actions for the (dilatonic) 0-branes through the compactification on a sphere are related to known two-dimensional dilaton gravity models. The SL(2,R) symmetry of the (generalized) conformal quantum mechanics is realized within such two-dimensional models. The two-dimensional dilatonic gravity model derived from the non-dilatonic 0-brane action is related to the Liouville theory and therefore is conformal, whereas the two-dimensional model derived from the dilatonic 0-brane action does not have the conformal symmetry.