The off-shell 4D/5D connection

TL;DR

This paper develops a systematic off-shell reduction scheme from five to four dimensions for supergravity theories with higher-derivative couplings, clarifying the structure of BPS black holes and revealing new supersymmetric invariants.

Contribution

It introduces a novel off-shell reduction method that decomposes 5D supergravity into 4D invariants, including a new invariant involving Ricci tensor squared.

Findings

Decomposition of 5D Weyl multiplet into 4D multiplets.

Identification of a new N=2 supersymmetric invariant with Ricci tensor squared.

Resolution of the relation between 5D Chern-Simons terms and 4D black holes.

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.