Supersymmetric asymptotically locally AdS${}_5$ gravitational solitons

We construct supersymmetric gravitational soliton solutions of five-dimensional gauged supergravity coupled to arbitrarily many vector multiplets. The solutions are complete, globally stationary, $1\mathrm{/}4$-BPS and are asymptotically locally AdS${}_5$ with conformal boundary $\mathbb{R}\times L(p,1)$. The construction uses an $SU(2)\times U(1)-$invariant ansatz originally used by Gutowski and Reall to construct supersymmetric asymptotically AdS${}_5$ black holes. A subset of these solutions have previously been obtained as supersymmetric limits of a class of local solutions of $U(1{)}^3$ gauged supergravity found by Chong-Cvetic-Lu-Pope, and by Lucietti-Ovchinnikov in their classification of $SU(2)$-invariant solutions of minimal gauged supergravity.