Dirac Singleton as a Relativistic Field Beyond Standard Model

TL;DR

This paper proposes a new interpretation of Dirac singletons as relativistic fields in higher-dimensional space-time, suggesting potential relevance to dark matter and baryon asymmetry in cosmology.

Contribution

It introduces a novel higher-dimensional field interpretation of Dirac singletons, differing from previous models, and explores their possible interactions with gravity and implications for cosmology.

Findings

Singletons form infinite-dimensional Lorentz group representations.

Singletons cannot be localized in ${d+1}$ dimensions, making them unobservable locally.

Potential relevance of singletons to dark matter and baryon asymmetry in a universe with dark energy.

Abstract

A new interpretation of Dirac singletons \cite{Dirac:1963ta}, i.e. free conformal fields in $d$ dimensions, as relativistic fields in a $d+1$-dimensional space-time with cosmological constant, that differs from the Flato-Fronsdal dipole construction in $AdS_{d+1}$ \cite{Flato:1986uh}, is proposed. The $d+1$-dimensional field is described at the level of both equations and Lagrangian. It forms an infinite-dimensional representation of the $d+1$-dimensional Lorentz group that relates fields at different space-time points. The associated well-known fact is that singleton cannot be localized at a point in ${d+1}$ dimensions, hence being unobservable via local scattering/radiation phenomena in the Standard Model ($d=3$). On the other hand, that singleton respects ${d+1}$ dimensional relativistic symmetries makes it possible to introduce its interactions with gravity and other relativistic fields in $d+1$ dimensions. It is speculated that the presence of singleton in a four-dimensional field theory with non-zero cosmological constant (dark energy) can be relevant to the dark matter phenomenon and baryon asymmetry generation.