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 AdSd vacua with a bridge admitting an AdSd+1 interpretation, the holographic dual is a CFTd with two CFTd−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.

De Luca, G., De Ponti, N., Mondino, A., Tomasiello, A. (2021). Cheeger bounds on spin-two fields. JOURNAL OF HIGH ENERGY PHYSICS, 2021(12) [10.1007/JHEP12(2021)217].

Cheeger bounds on spin-two fields

De Luca G. B.
;
Tomasiello A.
2021

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 AdSd vacua with a bridge admitting an AdSd+1 interpretation, the holographic dual is a CFTd with two CFTd−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.
Articolo in rivista - Articolo scientifico
Differential and Algebraic Geometry; p-branes; Spacetime Singularities; Superstring Vacua;
English
De Luca, G., De Ponti, N., Mondino, A., Tomasiello, A. (2021). Cheeger bounds on spin-two fields. JOURNAL OF HIGH ENERGY PHYSICS, 2021(12) [10.1007/JHEP12(2021)217].
De Luca, G; De Ponti, N; Mondino, A; Tomasiello, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/360256
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