Abstract
We show that κ-Poincaré invariant gauge theories on κ-Minkowski space with physically acceptable commutative (low energy) limit must be 5-d. The gauge invariance requirement of the action fixes the dimension of the κ-Minkowski space to d = 5 and selects the unique twisted differential calculus with which the construction can be achieved. We characterize a BRST symmetry related to the 5-d noncommutative gauge invariance though the definition of a nilpotent operation, which is used to construct a gauge-fixed action. We also consider standard scenarios assuming (compactification of) flat extra dimension, for which the 5-d deformation parameter κ can be viewed as the bulk 5-d Planck mass. We study physical properties of the resulting 4-d effective theories. Recent data from collider experiments require κ ≳ \( \mathcal{O} \)(1013) GeV. The use of standard test of in-vacuo dispersion relations of Gamma Ray Burst photons increases this lower bound by 4 orders of magnitude. The robustness of this bound is discussed in the light of possible new features of noncommutative causal structures.
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Dedicated to the memory of John Madore.
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Mathieu, P., Wallet, JC. Single extra dimension from κ-Poincaré and gauge invariance. J. High Energ. Phys. 2021, 209 (2021). https://doi.org/10.1007/JHEP03(2021)209
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DOI: https://doi.org/10.1007/JHEP03(2021)209