Cheeger bounds on spin-two fields. (English) Zbl 1521.83177
Summary: 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 \(\mathrm{AdS}_d\) vacua with a bridge admitting an \(\mathrm{AdS}_{d+1}\) interpretation, the holographic dual is a \(\mathrm{CFT}_d\) with two \(\mathrm{CFT}_{ d - 1}\) boundaries. The ratio of their degrees of freedom gives the graviton mass, generalizing results obtained by C. Bachas and I. Lavdas [J. High Energy Phys. 2018, No. 11, Paper No. 3, 22 p. (2018; Zbl 1471.83021)] 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.
MSC:
| 83E30 | String and superstring theories in gravitational theory |
| 83E50 | Supergravity |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83C75 | Space-time singularities, cosmic censorship, etc. |
Keywords:
differential and algebraic geometry; \(p\)-branes; spacetime singularities; superstring vacuaCitations:
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