Conformal group with two observer independent scales

TL;DR

This paper proposes a new relativistic framework with two observer-independent scales based on a deformed conformal algebra, introducing a non-commutative space-time and analyzing its implications for Lorentz invariance and quantum deformations.

Contribution

It introduces a conformal algebra deformation with two invariant scales, extending DSR theories and proposing a new non-commutative space-time structure.

Findings

Momentum space retains Lorentz invariance in a deformed sense.

The space-time generalizes $ppa$-Minkowski but breaks Lorentz invariance.

The formalism aids in understanding quantum deformations in AdS-CFT.

Abstract

The Poincar\'e sector of a recently deformed conformal algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, the symmetries of a new relativistic theory with two observer-independent scales (or DSR theory). Also a new non-commutative space-time is proposed. It is found that momentum space exhibits the same features of the DSR proposals preserving Lorentz invariance in a deformed way. The space-time sector is a generalization of the well known non-commutative $\kappa$-Minkowski space-time which however does not preserve Lorentz invariance, not even in the deformed sense. It is shown that this behavior could be expected in some attempts to construct DSR theories starting from the Poincar\'e sector of a deformed symmetry larger than Poincar\'e symmetry, unless one takes a variable Planck length. It is also shown that the formalism can be useful in analyzing the role of quantum deformations in the ``AdS-CFT correspondence".