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

TL;DR

The work identifies a space-time-uncertainty–driven conformal structure in D-particle matrix quantum mechanics, revealing an SU(1,1) symmetry generated by H, D, and K that constrains the dynamics under scaling and special conformal transformations. In the near-horizon regime, the same conformal structure persists in the classical D-particle background, allowing the 0+1D Yang–Mills theory to be interpreted as a boundary CFT and strengthening Maldacena’s conjecture for D-particle systems. The authors derive a recursive, symmetry-driven form for the D-particle interaction action that reproduces the known supergravity action and aligns with low-loop results, suggesting the duality extends beyond AdS-like settings. They also discuss limitations, potential extensions to other Dp-branes, and the prospects for deriving these symmetries directly from the matrix model and a background-independent formulation.

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.