Conformal Symmetry of Relativistic and Nonrelativistic Systems and AdS/CFT Correspondence

TL;DR

This paper explores the conformal symmetries of relativistic and nonrelativistic systems within the AdS/CFT framework, revealing how various systems can be related to particles in AdS spaces, thus unifying their symmetry properties.

Contribution

It demonstrates the nonlinear realization of conformal symmetries in different systems and establishes their connection to particles in AdS spaces, extending the AdS/CFT correspondence to nonrelativistic cases.

Findings

Massless particles in Minkowski space relate to AdS boundary systems.

Nonrelativistic systems can be mapped to particles in AdS_2 x S^{d-1}.

Various physical models share a common conformal symmetry structure.

Abstract

The nonlinear realization of conformal so(2,d) symmetry for relativistic systems and the dynamical conformal so(2,1) symmetry of nonrelativistic systems are investigated in the context of AdS/CFT correspondence. We show that the massless particle in d-dimensional Minkowski space can be treated as the system confined to the border of the AdS_{d+1} of infinite radius, while various nonrelativistic systems may be canonically related to a relativistic (massless, massive, or tachyon) particle on the AdS_2 X S^{d-1}. The list of nonrelativistic systems "unified" by such a correspondence comprises the conformal mechanics model, the planar charge-vortex and 3-dimensional charge-monopole systems, the particle in a planar gravitational field of a point massive source, and the conformal model associated with the charged particle propagating near the horizon of the extreme Reissner-Nordstrom black hole.