Gravitational actions in two dimensions and the Mabuchi functional

Frank Ferrari*, Semyon Klevtsov, Steve Zelditch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 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 languageEnglish (US)
Pages (from-to)341-369
Number of pages29
JournalNuclear Physics B
Volume859
Issue number3
DOIs
StatePublished - Jun 21 2012

Funding

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 Nucléaires (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 .

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Fingerprint

Dive into the research topics of 'Gravitational actions in two dimensions and the Mabuchi functional'. Together they form a unique fingerprint.

Cite this