2006/10/31 by Alex Giacomini, Ricardo Troncoso, Steven Willison
Physics and Astronomy · #Black Holes and Theoretical Physics #Connection (principal bundle) #Cosmology #Duality (order theory) #Extension (predicate logic) #Gauge theory #Gravitation #Noncommutative and Quantum Gravity Theories #Quantum and Classical Electrodynamics #Spin connection #Supergravity #Torsion (gastropod) #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/24/11/005
published as Class.Quant.Grav.24:2845-2860,2007 · LaTex 24 pages, no figures. Minor changes, references added. Accepted for publication on Class. Quant. Grav
arxiv created 2007/05/03 · openalex publication_date 2007/05/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first-order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein–Hilbert term with cosmological constant, the gravitational sector contains the Lorentz–Chern–Simons form and a term involving the torsion each with arbitrary couplings. The supersymmetric extension is carried out for vanishing and negative effective cosmological constant, and it is shown that the action can be written as a Chern–Simons theory for the supersymmetric extension of the Poincaré and AdS groups, respectively. Here we introduce a duality map between different gravity theories that greatly simplifies the construction. This map relies on the different ways to make geometry emerge from a single gauge potential. The extension for gravitini is also performed.