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

TL;DR

The paper addresses how conformal symmetry in relativistic and nonrelativistic contexts can be unified under the AdS/CFT framework. It develops an ambient $d+2$-dimensional massless model with constraints that realize the $so(2,d)$ Lorentz symmetry and, upon reduction, reproduces the $d$-dimensional conformal symmetry as observables. It then shows that a broad class of nonrelativistic conformal systems (including the AFF model, planar charge-vortex, charge-monopole, planar gravitational cone, and near-horizon RN-black-hole conformal dynamics) are canonically equivalent to relativistic particles on AdS$_2 imes S^{d-1}$, thereby unifying them under a holographic interpretation. Quantization translates the classical $so(2,1)$ structure into Schrödinger equations with hidden conformal symmetry, illuminating the holographic relationship and suggesting extensions to spin and superconformal theories, as well as connections to two-time physics.

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.