TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.5.134
TI  - Bubbling saddles of the gravitational index
PY  - 2025/11/24
UR  - https://www.scipost.org/SciPostPhys.19.5.134
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 5
SP  - 134
A1  - Cassani, Davide
AU  - Ruipérez, Alejandro
AU  - Turetta, Enrico
AB  - We consider the five-dimensional supergravity path integral that computes a supersymmetric index, and uncover a wealth of semiclassical saddles with bubbling topology. These are complex finite-temperature configurations asymptotic to $S^1×\mathbb{R}^4$, solving the supersymmetry equations. We assume a $\mathrm{U}(1)^3$ symmetry given by the thermal isometry and two rotations, and present a general construction based on a rod structure specifying the fixed loci of the $\mathrm{U}(1)$ isometries and their three-dimensional topology. These fixed loci may correspond to multiple horizons or three-dimensional bubbles, and they may have $S^3$, $S^2× S^1$, or lens space topology. Allowing for conical singularities gives additional topologies involving spindles and branched spheres or branched lens spaces. As a particularly significant example, we analyze in detail the configurations with a horizon and a bubble just outside of it. We determine the possible saddle-point contribution of these configurations to the gravitational index by evaluating their on-shell action and the relevant thermodynamic relations. We also spell out two limits leading to well-defined Lorentzian solutions. The first is the extremal limit, which gives the known BPS black ring and black lens solutions. The on-shell action and chemical potentials remain well-defined in this limit and should thus provide the contribution of the black ring and black lens to the gravitational index. The second is a limit leading to horizonless bubbling solutions, which have purely imaginary action.
ER  -

@Article{10.21468/SciPostPhys.19.5.134,
	title={{Bubbling saddles of the gravitational index}},
	author={Davide Cassani and Alejandro Ruipérez and Enrico Turetta},
	journal={SciPost Phys.},
	volume={19},
	pages={134},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.5.134},
	url={https://scipost.org/10.21468/SciPostPhys.19.5.134},
}