The off-shell 4D/5D connection

Abstract

A systematic off-shell reduction scheme from five to four space-time dimensions is presented for supergravity theories with eight supercharges. It is applicable to theories with higher-derivative couplings and it is used to address a number of open questions regarding BPS black holes in five dimensions. Under this reduction the 5D Weyl multiplet becomes reducible and decomposes into the 4D Weyl multiplet and an extra Kaluza-Klein vector multiplet. The emergence of the pseudoscalar field of the latter multiplet and the emergence of the 4D R-symmetry group are subtle features of the reduction. The reduction scheme enables to determine how a 5D supersymmetric Lagrangian with higher-derivative couplings decomposes upon dimensional reduction into a variety of independent 4D supersymmetric invariants, without the need for imposing field equations. In this way we establish, for example, the existence of a new N=2 supersymmetric invariant that involves the square of the Ricci tensor. Finally we resolve the questions associated with the 5D Chern-Simons terms for spinning BPS black holes and their relation to the corresponding 4D black holes.

35 pages; minor text changes and one more reference

References in corpus (4)

• Supersymmetric Completion of an R^2 Term in Five-Dimensional Supergravity
• String Theory Effects on Five-Dimensional Black Hole Physics
• New supersymmetric higher-derivative couplings: Full N=2 superspace does not count!
• Comments on Charges and Near-Horizon Data of Black Rings

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• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• $R^2$ corrected AdS${}_2$ holography
• The gravitational index of 5d black holes and black strings
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• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
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