### Abstract

We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation introduces 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. dS_{4} or AdS_{4}. 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 dS_{4} takes the form of so(5, 1), while for AdS_{4} 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.

Original language | English (US) |
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Pages (from-to) | 58-74 |

Number of pages | 17 |

Journal | Nuclear Physics B |

Volume | 894 |

DOIs | |

State | Published - May 1 2015 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics B*,

*894*, 58-74. https://doi.org/10.1016/j.nuclphysb.2015.02.018