Massive and massless particles in Mielke-Baekler geometries
4 affiliations
- 1Universitat Politècnica de Catalunya, EPSEVG
- 2University of Florence and INFN
- 3The University of Edinburgh
- 4Universitat de Barcelona
Abstract
A bstract : The Mielke-Baekler geometries are three-dimensional reductive homogeneous spacetimes together with a choice of invariant connection which is compatible with a lorentzian metric. The spacetimes generalise Minkowski and (anti)de Sitter spacetimes in that the invariant metric connection can have torsion, a peculiarity of three dimensions. Using coadjoint orbits and the techniques of nonlinear realisations, we construct worldline actions for massive and massless spinning particles moving in these spacetimes. We pay particular attention to the so-called teleparallel branch, in which the curvature of the invariant connection vanishes. Apart from the trivial Minkowski case, this singles out anti-de Sitter spacetime, as the only of these lorentzian manifolds admitting an invariant Weitzenböck connection; that is, a flat connection with torsion. The introduction of a Wess-Zumino term describing spin has, as a main consequence, the appearance of dynamical sectors (denoted “regular” and “critical”), with a different number of physical degrees of freedom. In particular, in the massive case, we discuss the formulation of the dynamics in terms of either the Weitzenböck or the Levi-Civita connection, and the emergence of a Papapetrou-type forcing term in the critical sector. For the massless particle we study the Noether symmetries of the action, which, for the spinless case, include the conformal transformations. For nonzero spin, only the Killing subset survives as genuine Noether transformations in the regular sector, while in the critical sector any conformal Killing contribution can be set to zero by a gauge transformation.
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BibTeX
@article{batlle2026massive,
title = {{Massive and massless particles in Mielke-Baekler geometries}},
author = {Carles Batlle and Roberto Casalbuoni and Daniele Dominici and José Figueroa-O’Farrill and Joaquim Gomis},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)229},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)229},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Massive and massless particles in Mielke-Baekler geometries
AU - Carles Batlle
AU - Roberto Casalbuoni
AU - Daniele Dominici
AU - José Figueroa-O’Farrill
AU - Joaquim Gomis
PY - 2026
DA - 2026/10/22
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)229
UR - https://link.springer.com/article/10.1007/JHEP10(2026)229
AB - A bstract : The Mielke-Baekler geometries are three-dimensional reductive homogeneous spacetimes together with a choice of invariant connection which is compatible with a lorentzian metric. The spacetimes generalise Minkowski and (anti)de Sitter spacetimes in that the invariant metric connection can have torsion, a peculiarity of three dimensions. Using coadjoint orbits and the techniques of nonlinear realisations, we construct worldline actions for massive and massless spinning particles moving in these spacetimes. We pay particular attention to the so-called teleparallel branch, in which the curvature of the invariant connection vanishes. Apart from the trivial Minkowski case, this singles out anti-de Sitter spacetime, as the only of these lorentzian manifolds admitting an invariant Weitzenböck connection; that is, a flat connection with torsion. The introduction of a Wess-Zumino term describing spin has, as a main consequence, the appearance of dynamical sectors (denoted “regular” and “critical”), with a different number of physical degrees of freedom. In particular, in the massive case, we discuss the formulation of the dynamics in terms of either the Weitzenböck or the Levi-Civita connection, and the emergence of a Papapetrou-type forcing term in the critical sector. For the massless particle we study the Noether symmetries of the action, which, for the spinless case, include the conformal transformations. For nonzero spin, only the Killing subset survives as genuine Noether transformations in the regular sector, while in the critical sector any conformal Killing contribution can be set to zero by a gauge transformation.
SN - 1029-8479
ER -