Abstract
We present a gauge theory of the conformal group in four spacetime dimensions with a nonvanishing torsion. In particular, we allow for a completely antisymmetric torsion, equivalent by Hodge duality to an axial vector whose presence does not spoil the conformal invariance of the theory, in contrast with claims of antecedent literature. The requirement of conformal invariance implies a differential condition (in particular, a Killing equation) on the aforementioned axial vector, which leads to a Maxwell-like equation in a four-dimensional curved background. We also give some preliminary results in the context of four-dimensional conformal supergravity in the geometric approach, showing that if we only allow for the constraint of vanishing supertorsion, all the other constraints imposed in the spacetime approach are a consequence of the closure of the Bianchi identities in superspace. This paves the way towards a future complete investigation of the conformal supergravity using the Bianchi identities in the presence of a nonvanishing (super)torsion.
- Received 11 April 2021
- Accepted 3 September 2021
DOI:https://doi.org/10.1103/PhysRevD.104.084034
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society