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

18 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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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