Cheeger bounds on spin-two fields
arXiv:2109.11560 · doi:10.1007/JHEP12(2021)217
Abstract
We consider gravity compactifications whose internal space consists of small bridges connecting larger manifolds, possibly noncompact. We prove that, under rather general assumptions, this leads to a massive spin-two field with very small mass. The argument involves a recently-noticed relation to Bakry--Émery geometry, a version of the so-called Cheeger constant, and the theory of synthetic Ricci lower bounds. The latter technique allows generalizations to non-smooth spaces such as those with D-brane singularities. For AdS vacua with a bridge admitting an AdS interpretation, the holographic dual is a CFT with two CFT boundaries. The ratio of their degrees of freedom gives the graviton mass, generalizing results obtained by Bachas and Lavdas for . We also prove new bounds on the higher eigenvalues. These are in agreement with the spin-two swampland conjecture in the regime where the background is scale-separated; in the opposite regime we provide examples where they are in naive tension with it.
61 pages, 4 figures
References in corpus (12)
- Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
- Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
- Four-Dimensional SCFTs from M5-Branes
- Spin-2 spectrum of defect theories
- Islands and Page curves in 4d from Type IIB
- Universal RG Flows Across Dimensions and Holography
- Cosmology from confinement?
- Braneworld localisation in hyperbolic spacetime
- An optimal dimension-free upper bound for eigenvalue ratios
- Leaps and bounds towards scale separation
- Bootstrap Bounds on Closed Hyperbolic Manifolds
- Massive AdS Supergravitons and Holography