Unified Geometric Theory of Gravity and Supergravity
Abstract
A unified geometric formulation of gravitation and supergravity is presented. The action for these theories is constructed out of the components of the curvature tensor for bundle spaces with four-dimensional Lorentz base manifold and structure groups Sp(4) for gravity and OSp(1,4) for supergravity. The requirement of invariance under reflections, local Lorentz transformations, and general coordinate transformations uniquely determines the action and ensures the existence of local supersymmetry in supergravity.
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The McDowell-Mansouri formulation of general relativity provides an action of gravity consisting of a BF term plus a genuine potential term rather than constraints.
“The interest of the latter formulation is that it provides an action of gravity that is given by a BF term plus a genuine potential term instead of constraints.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [259]
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- Authors
- MacDowell, S. W., & Mansouri, F.
- Affiliations
- Yale University (US)
- ORCID
- Mansouri, F.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1977-04-04
- Volume
- 38
- Issue
- 14
- Pages
- 739-742
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2142318758
- Cited by
- 737
- References
- 8
- Citations by year
- 2026: 24 · 2025: 27 · 2024: 18 · 2023: 28 · 2022: 25 · 2021: 30 · 2020: 18 · 2019: 13 · 2018: 30 · 2017: 31 · 2016: 21 · 2015: 16 · 2014: 25 · 2013: 17 · 2012: 23
- FWCI
- 53.72
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- supergravity, gravity, curvature tensor, local supersymmetry, local Lorentz transformations, general coordinate transformations, reflection invariance, Hamilton's principle
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