All supersymmetric solutions of minimal supergravity in five dimensions

TL;DR

This work delivers the first complete classification of supersymmetric solutions in minimal five-dimensional supergravity, splitting into timelike and null branches and expressing the full timelike class in terms of a hyper-Kähler base with data (B,f,ω) and the null class as plane-fronted waves governed by harmonic functions on R^3. It provides numerous explicit solutions, including a Gödel-type universe and a broad family of plane waves, and shows how these five-dimensional geometries uplift to higher-dimensional theories, notably yielding a Gödel solution in D=11 with 20 preserved supersymmetries. The analysis ties the solutions to G-structures (SU(2) in the timelike case and R^3 in the null case) and demonstrates that all maximally supersymmetric cases arise from special GH-base configurations, including AdS_2×S^3, AdS_3×S^2, near-horizon BMPV, and plane waves. The results offer a concrete, constructive framework for generating and understanding supersymmetric backgrounds in higher-dimensional supergravity, with implications for string theory, black hole physics, and holography. They also illustrate the surprising persistence of closed timelike curves in supersymmetric spacetimes and motivate further exploration of gauged theories and higher-dimensional generalizations.

Abstract

All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified. The solutions preserve either one half or all of the supersymmetry. Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the Gödel universe which lifts to a solution of eleven dimensional supergravity that preserves 20 supersymmetries.