Planck-scale phenomenology with anti-de Sitter momentum space

Understand

We investigate the anti-de Sitter (AdS) counterpart to the well studied de Sitter (dS) model for energy-momentum space, viz "$\kappa$-momentum space" space (with a structure based on the properties of the $\kappa$-Poincar\'e Hopf algebra).

• On the basis of previous preliminary results one might expect the two models to be "dual": dS exhibiting an invariant maximal spatial momentum but unbounded energy, AdS a maximal energy but unbounded momentum.
• If that were the case AdS momentum space could be used to implement a principle of maximal Planck-scale energy, just as several studies use dS momentum space to postulate of maximal Planck-scale spatial momentum.
• However several unexpected features are uncovered in this paper, which limit the scope of the expected duality, and interestingly they take different forms in different coordinatizations of AdS momentum space.