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  A note on the double dual graviton

Henneaux, M., Lekeu, V., & Amaury, L. (2020). A note on the double dual graviton. Journal of Physics A, 53(1): 014002. doi:10.1088/1751-8121/ab56ed.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0004-DB40-D Version Permalink: http://hdl.handle.net/21.11116/0000-0005-A59D-0
Genre: Journal Article

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 Creators:
Henneaux, Marc, Author
Lekeu, Victor, Author
Amaury, Leonard1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: High Energy Physics - Theory, hep-th
 Abstract: The (free) graviton admits, in addition to the standard Pauli-Fierz description by means of a rank-two symmetric tensor, a description in which one dualizes the corresponding (2,2)-curvature tensor on one column to get a (D-2,2)-tensor, where D is the spacetime dimension. This tensor derives from a gauge field with mixed Yound symmetry (D-3,1) called the "dual graviton" field. The dual graviton field is related non-locally to the Pauli-Fierz field (even on-shell), in much the same way as a p-form potential and its dual (D-p-2)-form potential are related in the theory of an abelian p-form. Since the Pauli-Fierz field has a Young tableau with two columns (of one box each), one can contemplate a double dual description in which one dualizes on both columns and not just on one. The double dual curvature is now a (D-2,D-2)-tensor and derives from a gauge field with (D-3, D-3) mixed Young symmetry, the "double dual graviton" field. We show, however, that the double dual graviton field is algebraically and locally related to the original Pauli-Fierz field and, so, does not provide a truly new description of the graviton. From this point of view, it plays a very different role from the dual graviton field obtained through a single dualization. We also show that these equations can be obtained from a variational principle in which the variables to be varied in the action are (all) the components of the double-dual field as well as an auxiliary field with (2,1) Young symmetry. By gauge fixing the shift symmetries of this action principle, one recovers the Pauli-Fierz action. Our approach differs from the interesting approach based on parent actions and covers only the free, sourceless theory. Similar results are argued to hold for higher spin gauge fields.

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 Dates: 2019-09-272019-10-042020
 Publication Status: Published in print
 Pages: v2: some clarifications and updated references. 13 pages. Submitted for publication in the memorial volume for Peter Freund
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 Identifiers: arXiv: 1909.12706
URI: http://arxiv.org/abs/1909.12706
DOI: 10.1088/1751-8121/ab56ed
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Title: Journal of Physics A
Source Genre: Journal
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Pages: - Volume / Issue: 53 (1) Sequence Number: 014002 Start / End Page: - Identifier: -