Manifest electric-magnetic duality in linearized conformal gravity
Abstract
We derive a manifestly duality-symmetric formulation of the action principle for conformal gravity linearized around Minkowski space-time. The analysis is performed in the Hamiltonian formulation, the fourth-order character of the equations of motion requiring the formal treatment of the three-dimensional metric perturbation and the extrinsic curvature as independent dynamical variables. The constraints are solved in terms of two symmetric potentials that are interpreted as a dual three-dimensional metric and a dual extrinsic curvature. The action principle can be written in terms of these four dynamical variables, duality acting as simultaneous rotations in the respective spaces spanned by the three-dimensional metrics and the extrinsic curvatures. A twisted self-duality formulation of the equations of motion is also provided.
- Publication:
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Physical Review D
- Pub Date:
- May 2021
- DOI:
- 10.1103/PhysRevD.103.105014
- arXiv:
- arXiv:2101.04705
- Bibcode:
- 2021PhRvD.103j5014F
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- Phys. Rev. D 103, 105014 (2021)