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Title: Cheeger bounds on spin-two fields
A bstract 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 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.  more » « less
Award ID(s):
2014215
PAR ID:
10352502
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2021
Issue:
12
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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