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Conformal symmetry of relativistic and nonrelativistic systems and AdS/CFT correspondence.(English)Zbl 1040.81070

Summary: 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\(_2{\times}S^{d-1}\). The list of nonrelativistic systems “unified” by such a correspondence comprises the conformal mechanics model, the planar charge-vortex and three-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-Nordström black hole.

MSC:

81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83C57 Black holes
83C47 Methods of quantum field theory in general relativity and gravitational theory

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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