Space-Time Uncertainty Principle and Conformal Symmetry in D-Particle Dynamics

TL;DR

This paper demonstrates a conformal symmetry in D-particle dynamics inspired by the space-time uncertainty principle, supporting the gauge/gravity duality conjecture by linking supergravity and supersymmetric Yang-Mills models.

Contribution

It establishes a conformal symmetry in D-particle dynamics and derives the effective action, providing evidence for the Maldacena conjecture in the context of D-particles.

Findings

Conformal symmetry is shown in D-particle dynamics.

The effective action is uniquely determined by symmetry principles.

Supports the gauge/gravity duality for D-particles.

Abstract

Motivated by the space-time uncertainty principle, we establish a conformal symmetry in the dynamics of D-particles. The conformal symmetry, combined with the supersymmetric non-renormalization theorem, uniquely determines the classical form of the effective action for a probe D-particle in the background of a heavy D-particle source, previously constructed by Becker-Becker-Polchinski-Tseytlin. Our results strengthen the conjecture proposed by Maldacena on the correspondence, in the case of D-particles, between the supergravity and the supersymmetric Yang-Mills matrix models in the large $N$-limit, the latter being the boundary conformal field theory of the former in the classical D-particle background in the near horizon limit.