Single Extra Dimension from $\kappa$-Poincaré and Gauge Invariance

Abstract

We show that $\kappa$-Poincaré invariant gauge theories on $\kappa$-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 $\kappa$-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 $\kappa$ 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 $\kappa \gtrsim \mathcal{O}(10^{13})\text{GeV}$. 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.

Expanded version. Physical discussion added. Various misprints corrected, reference updated.24 pages. To appear in JHEP