Who Ordered the Anti-de Sitter Tangent Group?

TL;DR

This paper investigates different tangent groups in general relativity and demonstrates that only the anti-de Sitter tangent group meets all physical consistency criteria, unlike Lorentz and de Sitter groups.

Contribution

It establishes the anti-de Sitter tangent group as the unique consistent choice for formulating general relativity with fermionic representations.

Findings

Anti-de Sitter tangent group is consistent with physical requirements.

Lorentz and de Sitter tangent groups are incompatible with all physical requirements.

The formulation of general relativity can be unambiguously done with the anti-de Sitter tangent group.

Abstract

General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations. We show that besides of the Lorentz group only anti-de Sitter tangent group is consistent with all physical requirements.