Covariant Non-Commutative Space-Time

2014/01/08 by Jonathan Heckman, Herman Verlinde · 1 citation
Physics and Astronomy · #gr-qc #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2015.02.018

20 pages, 1 figure

arxiv created 2014/01/08 · arxiv updated 2015/06/18

Abstract

We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation depends on a short-distance scale ℓ_p, and thus breaks scale invariance, but preserves all space-time isometries. The non-commutative algebra is defined on space-times with non-zero constant curvature, i.e. dS₄ or AdS₄. The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor. The polarization tensor takes active part in the non-commutative algebra, which for dS₄ takes the form of so(5,1), while for AdS₄ it assembles into so(4,2). The structure of the non-commutative correlation functions hints that the deformed theory contains gravitational interactions and a Regge-like trajectory of higher spin excitations.

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• Dual κ-Minkowski spaces and κ-Poincaré algebras from Yang model and their Weyl realizations

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