Some encouraging and some cautionary remarks on Doubly Special Relativity in Quantum Gravity

TL;DR

The paper reviews the prospects and challenges of implementing Doubly Special Relativity (DSR) in quantum gravity, highlighting recent developments, open issues, and conceptual conflicts in various models including Loop Quantum Gravity and noncommutative spacetimes.

Contribution

It critically examines the current state of DSR in quantum gravity, identifying promising directions and unresolved conceptual and technical issues.

Findings

Emergence of DSR in Loop Quantum Gravity is promising but relies on unverified assumptions.

$oldsymbol{ ext{kappa}}$-Poincaré algebra elements are promising but have unresolved issues, especially in two-particle sectors.

Certain 2+1-dimensional gravity structures may conflict with DSR principles.

Abstract

The idea of a role for DSR (doubly-special relativity) in quantum gravity finds some encouragement in a few scenarios, but in order to explore some key conceptual issues it is necessary to find a well-understood toy-quantum-gravity model that is fully compatible with the DSR principles. Perhaps the most significant source of encouragement comes from the recent proposal of a path for the emergence of DSR in Loop Quantum Gravity, which however relies on a few assumptions on the results of some computations that we are still unable to perform. Indications in favor of the possibility of using some elements of $\kappa$-Poincar\'e Hopf algebras (and of the related $\kappa$-Minkowski noncommutative spacetime) for the construction of a DSR theory have been discussed extensively, but a few stubborn open issues must still be resolved, especially in the two-particle sector. It has been recently observed that certain structures encountered in a formulation of 2+1-dimensional classical-gravity models would fit naturally in a DSR framework, but some key elements of these 2+1-dimensional models, including the description of observers, might be incompatible with the DSR principles.