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arXiv · 2109.11560

Cheeger bounds on spin-two fields

G. Bruno De Luca·Nicolò De Ponti·Andrea Mondino·Alessandro Tomasiello
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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--\'Emery 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$_d$ vacua with a bridge admitting an AdS$_{d+1}$ interpretation, the holographic dual is a CFT$_d$ with two CFT$_{d-1}$ boundaries. The ratio of their degrees of freedom gives the graviton mass, generalizing results obtained by Bachas and Lavdas for $d=4$. 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.

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G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino, Alessandro Tomasiello. 2021-09-23. Cheeger bounds on spin-two fields. https://doi.org/10.1007/jhep12(2021)217

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