Propagating torsion in the Einstein frame

TL;DR

This paper reformulates the Einstein-Cartan-Saa theory of torsion in the Einstein conformal frame, addressing energy positivity issues and deriving a modified propagating torsion theory with electromagnetic interactions.

Contribution

It introduces a reformulation of torsion theory in the Einstein frame and derives a new propagating torsion model with electromagnetic coupling.

Findings

Reformulation ensures energy positivity for torsion.

Derivation of a modified torsion kinetic term with electromagnetic fields.

Establishment of constraints linking torsion, connection, and gauge invariance.

Abstract

The Einstein-Cartan-Saa theory of torsion modifies the spacetime volume element so that it is compatible with the connection. The condition of connection compatibility gives constraints on torsion, which are also necessary for the consistence of torsion, minimal coupling, and electromagnetic gauge invariance. To solve the problem of positivity of energy associated with the torsionic scalar, we reformulate this theory in the Einstein conformal frame. In the presence of the electromagnetic field, we obtain the Hojman-Rosenbaum-Ryan-Shepley theory of propagating torsion with a different factor in the torsionic kinetic term.