The off-shell 4D/5D connection. (English) Zbl 1309.81143
Summary: 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 4\(D\) R-symmetry group are subtle features of the reduction. The reduction scheme enables to determine how a 5\(D\) 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 4\(D\) black holes.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 83E50 | Supergravity |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
| 58J28 | Eta-invariants, Chern-Simons invariants |
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