Gravity from thermodynamics: Optimal transport and negative effective dimensions

De Luca, Giuseppe Bruno; De Ponti, Nicolò; Mondino, Andrea; Tomasiello, Alessandro

doi:10.21468/SciPostPhys.15.2.039

SciPost Physics

Gravity from thermodynamics: Optimal transport and negative effective dimensions

Giuseppe Bruno De Luca, Nicolò De Ponti, Andrea Mondino, Alessandro Tomasiello

SciPost Phys. 15, 039 (2023) · published 1 August 2023

doi: 10.21468/SciPostPhys.15.2.039
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Abstract

We prove an equivalence between the classical equations of motion governing vacuum gravity compactifications (and more general warped-product spacetimes) and a concavity property of entropy under time evolution. This is obtained by linking the theory of optimal transport to the Raychaudhuri equation in the internal space, where the warp factor introduces effective notions of curvature and (negative) internal dimension. When the Reduced Energy Condition is satisfied, concavity can be characterized in terms of the cosmological constant $\Lambda$; as a consequence, the masses of the spin-two Kaluza-Klein fields obey bounds in terms of $\Lambda$ alone. We show that some Cheeger bounds on the KK spectrum hold even without assuming synthetic Ricci lower bounds, in the large class of infinitesimally Hilbertian metric measure spaces, which includes D-brane and O-plane singularities. As an application, we show how some approximate string theory solutions in the literature achieve scale separation, and we construct a new explicit parametrically scale-separated AdS solution of M-theory supported by Casimir energy.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.2.039
TI  - Gravity from thermodynamics: Optimal transport and negative effective dimensions
PY  - 2023/08/01
UR  - https://www.scipost.org/SciPostPhys.15.2.039
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 2
SP  - 039
A1  - De Luca, Giuseppe Bruno
AU  - De Ponti, Nicolò
AU  - Mondino, Andrea
AU  - Tomasiello, Alessandro
AB  - We prove an equivalence between the classical equations of motion governing vacuum gravity compactifications (and more general warped-product spacetimes) and a concavity property of entropy under time evolution. This is obtained by linking the theory of optimal transport to the Raychaudhuri equation in the internal space, where the warp factor introduces effective notions of curvature and (negative) internal dimension. When the Reduced Energy Condition is satisfied, concavity can be characterized in terms of the cosmological constant $\Lambda$; as a consequence, the masses of the spin-two Kaluza-Klein fields obey bounds in terms of $\Lambda$ alone. We show that some Cheeger bounds on the KK spectrum hold even without assuming synthetic Ricci lower bounds, in the large class of infinitesimally Hilbertian metric measure spaces, which includes D-brane and O-plane singularities. As an application, we show how some approximate string theory solutions in the literature achieve scale separation, and we construct a new explicit parametrically scale-separated AdS solution of M-theory supported by Casimir energy.
ER  -

@Article{10.21468/SciPostPhys.15.2.039,
	title={{Gravity from thermodynamics: Optimal transport and negative effective dimensions}},
	author={Giuseppe Bruno De Luca and Nicolò De Ponti and Andrea Mondino and Alessandro Tomasiello},
	journal={SciPost Phys.},
	volume={15},
	pages={039},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.2.039},
	url={https://scipost.org/10.21468/SciPostPhys.15.2.039},
}

Cited by 4

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Giuseppe Bruno De Luca,
² Nicolò De Ponti,
³ Andrea Mondino,
⁴ Alessandro Tomasiello

Funders for the research work leading to this publication

European Research Council [ERC]
Instituto Nazionale di Fisica Nucleare (INFN) (through Organization: Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN])
Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) (through Organization: Ministero dell'Istruzione, dell'Università e della Ricerca / Ministry of Education, Universities and Research [MIUR])
Simons Foundation