Duality in linearized gravity

Details Duality in linearized gravity Duality in linearized gravity

2004-08-31

arxiv.org/abs/gr-qc/0408101v2

Phys.Rev. D71 (2005) 024018

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages; introduction rewritten and references added

Scientific paper

10.1103/PhysRevD.71.024018

We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of the action and not just symmetries of the equations of motion. Our approach relies on the introduction of two "superpotentials", one for the spatial components of the spin-2 field and the other for their canonically conjugate momenta. These superpotentials are two-index, symmetric tensors. They can be taken to be the basic dynamical fields and appear locally in the action. They are simply rotated into each other under duality. In terms of the superpotentials, the canonical generator of duality rotations is found to have a Chern-Simons like structure, as in the Maxwell case.

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