1995/11/14 by Kiyoshi Ezawa · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Formalism (music) #Gravitation #Lorentz group #Lorentz transformation #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Supergravity #Supersymmetry #Theoretical physics #hep-th
paper · pdf · doi:10.1143/ptp.95.863
published as Prog.Theor.Phys. 95 (1996) 863-882 · 26 pages Latex (references added)
arxiv created 1995/11/14 · openalex publication_date 1996/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is known that Ashtekar's formulation for pure Einstein gravity can be cast into the form of a topological field theory, namely, the SU(2) BF theory, with the two-form fields subject to an algebraic constraint. We extend this relation between Ashtekar's formalism and BF theories to N = 1 and N = 2 supergravities. The relevant gauge groups in these cases become graded Lie groups of SU(2), which are generated by left-handed local Lorentz transformations and left-supersymmetry transformations. As a corollary of these relations, we provide topological solutions for N = 2 supergravity with a vanishing cosmological constant. It is also shown that, due to the algebraic constraints, the Kalb-Ramond symmetry which is characteristic of BF theories breaks down to the symmetry under diffeomorphisms and right-supersymmetry transformations.