Gravitational actions in two dimensions and the Mabuchi functional

Frank Ferrari; Semyon Klevtsov; Steve Zelditch

doi:10.1016/j.nuclphysb.2012.02.003

Gravitational actions in two dimensions and the Mabuchi functional

Frank Ferrari^*, Semyon Klevtsov, Steve Zelditch

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

The Mabuchi energy is an interesting geometric functional on the space of Kähler metrics that plays a crucial rôle in the study of the geometry of Kähler manifolds. We show that this functional, as well as other related geometric actions, contribute to the effective gravitational action when a massive scalar field is coupled to gravity in two dimensions in a small mass expansion. This yields new theories of two-dimensional quantum gravity generalizing the standard Liouville models.

Original language	English (US)
Pages (from-to)	341-369
Number of pages	29
Journal	Nuclear Physics B
Volume	859
Issue number	3
DOIs	https://doi.org/10.1016/j.nuclphysb.2012.02.003
State	Published - Jun 21 2012

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.nuclphysb.2012.02.003

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title = "Gravitational actions in two dimensions and the Mabuchi functional",

abstract = "The Mabuchi energy is an interesting geometric functional on the space of K{\"a}hler metrics that plays a crucial r{\^o}le in the study of the geometry of K{\"a}hler manifolds. We show that this functional, as well as other related geometric actions, contribute to the effective gravitational action when a massive scalar field is coupled to gravity in two dimensions in a small mass expansion. This yields new theories of two-dimensional quantum gravity generalizing the standard Liouville models.",

author = "Frank Ferrari and Semyon Klevtsov and Steve Zelditch",

note = "Funding Information: This work is supported in part by the Belgian Fonds de la Recherche Fondamentale Collective (grant 2.4655.07 ), the Belgian Institut Interuniversitaire des Sciences Nucl{\'e}aires (grant 4.4505.86 ), the Interuniversity Attraction Poles Programme (Belgian Science Policy) , the Russian RFFI grant 11-01-00962 and the American NSF grant DMS-0904252 . ",

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AU - Ferrari, Frank

AU - Klevtsov, Semyon

AU - Zelditch, Steve

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Gravitational actions in two dimensions and the Mabuchi functional

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