Speaker
Description
I will discuss a large class of supersymmetric solutions of Euclidean five-dimensional supergravity recently studied in 2507.12650 [hep-th]. These solutions admit an interpretation as saddle points of the gravitational path integral that computes a supersymmetric index. They possess a $\mathrm{U}(1)^3$ isometry and are characterized by a rod structure specifying the fixed loci of the $\mathrm{U}(1)$ isometries. These fixed loci can correspond either to horizons or to three-dimensional bubbles, and may have $S^3, S^1 \times S^2$, or lens-space topology. I will then focus on configurations containing a single horizon together with a bubble outside it, and show that these geometries correspond to saddles carrying the entropy of supersymmetric black rings and black lenses. Finally, time permitting, I will discuss a decoupling limit leading to asymptotically $\mathrm{AdS}_3$ solutions, and argue that a subclass of our geometries provides saddle points of the $\mathrm{AdS}_3$ gravitational path integral computing the elliptic genus of the dual $\mathrm{CFT}_2$.