N=2 supergravity in five dimensions revisited

TL;DR

This work constructs matter-coupled $N=2$ supergravity in five dimensions using the superconformal approach, incorporating an arbitrary number of vector-, tensor-, and hypermultiplets and, crucially, allowing off-diagonal vector–tensor couplings. After gauge-fixing the superconformal symmetries to Poincaré, the authors derive the most general $N=2$, $D=5$ action with a bosonic sector suitable for BPS analyses and flux-compactification contexts, with couplings governed by a symmetric tensor ${ m ilde{C}}_{ ilde{I} ilde{J} ilde{K}}$, a symplectic metric $oldsymbol{ m ilde{oldsymbol{eta}}}_{MN}$, and the representation matrices $t_{I ilde{J}}{}^{ ilde{K}}$. The geometry of the hypermultiplet sector is treated via hypercomplex/hyper-Kähler to quaternionic-Kähler structures, including moment maps and SU(2) connections, and the vector sector obeys very special real geometry, all linked through the gauge-fixing map. The results generalize previous formulations by incorporating nontrivial vector–tensor couplings, enabling systematic searches for BPS domain walls, black holes, and Calabi–Yau flux vacua in M-theory compactifications. The work also discusses potential extensions to non-action conformal theories and alternative Weyl multiplets, highlighting rich avenues for future exploration.

Abstract

We construct matter-coupled N=2 supergravity in five dimensions, using the superconformal approach. For the matter sector we take an arbitrary number of vector-, tensor- and hyper-multiplets. By allowing off-diagonal vector-tensor couplings we find more general results than currently known in the literature. Our results provide the appropriate starting point for a systematic search for BPS solutions, and for applications of M-theory compactifications on Calabi-Yau manifolds with fluxes.

Figures (1)

• Figure 1: The gauge-fixing procedure: the underlined fields are eliminated when passing to Poincaré SUGRA. The arrows indicate how these fields are eliminated: by gauge-fixing a symmetry or by applying an equation of motion.