Doubly-Special Relativity: Facts, Myths and Some Key Open Issues

TL;DR

This paper reviews the current status, key open issues, and phenomenological relevance of doubly-special relativity theories, which incorporate invariant velocity and length scales, and clarifies misconceptions about their structure and variants.

Contribution

It provides a comprehensive analysis of different DSR scenarios, clarifies their theoretical structures, and distinguishes between true DSR theories and related but distinct models.

Findings

Some DSR scenarios do not modify dispersion relations.

Certain models with invariant scales are not true DSR theories.

Observable relativistic features can be insensitive to nonlinear symmetry redefinitions.

Abstract

I report, emphasizing some key open issues and some aspects that are particularly relevant for phenomenology, on the status of the development of "doubly-special" relativistic ("DSR") theories with both an observer-independent high-velocity scale and an observer-independent small-length/large-momentum scale, possibly relevant for the Planck-scale/quantum-gravity realm. I also give a true/false characterization of the structure of these theories. In particular, I discuss a DSR scenario without modification of the energy-momentum dispersion relation and without the $\kappa$-Poincar\'e Hopf algebra, a scenario with deformed Poincar\'e symmetries which is not a DSR scenario, some scenarios with both an invariant length scale and an invariant velocity scale which are not DSR scenarios, and a DSR scenario in which it is easy to verify that some observable relativistic (but non-special-relativistic) features are insensitive to possible nonlinear redefinitions of symmetry generators.