Constraining Torsion in Maximally symmetric (sub)spaces

TL;DR

This paper investigates how torsion behaves under space-time symmetries, especially in maximally symmetric spaces and subspaces, revealing constraints and equivalences for antisymmetric torsion tensors.

Contribution

It derives constraints on torsion in maximally symmetric spaces and shows an equivalence between different theoretical schemes for antisymmetric torsion.

Findings

Antisymmetric torsion components are constrained by symmetry.

An equivalence exists between schemes for antisymmetric torsion.

Constraints apply to both full spaces and subspaces.

Abstract

We look into the general aspects of space-time symmetries in presence of torsion, and how the latter is affected by such symmetries. Focusing in particular to space-times which either exhibit maximal symmetry on their own, or could be decomposed to maximally symmetric subspaces, we work out the constraints on torsion in two different theoretical schemes. We show that at least for a completely antisymmetric torsion tensor (for e.g. the one motivated from string theory), an equivalence is set between these two schemes, as the non-vanishing independent torsion tensor components turn out to be the same.