Year: 2026
Type: preprint
Abstract: We derive the necessary and sufficient conditions for AdS$_4$ solutions of $d=11$ supergravity to preserve ${\mathcal{N}} \leq 3$ supersymmetry. We use our setup to first impose ${\mathcal{N}}=2$ supersymmetry, recovering a previously known class of solutions, providing a non-trivial consistency of our equations. We then focus on the ${\mathcal{N}} = 3 $ case, first deriving the Tri-Sasaki class and then proving its uniqueness as the only ${\mathcal{N}} = 3$ AdS$_4$ class in eleven dimensional supergravity. Our work proves that all supersymmetric AdS$_4$ solutions preserving ${\mathcal{N}} > 2 $ supersymmetry are necessarily of Tri-Sasaki type.
Source: arXiv (Cornell University)
Author: Conti, Andrea
Institution: Universidad de Oviedo
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216005432