Gravitational actions in two dimensions and the Mabuchi functional

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 massi...

Full description

Saved in:
Bibliographic Details
Published in:Nuclear physics. B 2012-06, Vol.859 (3), p.341-369
Main Authors: Ferrari, Frank, Klevtsov, Semyon, Zelditch, Steve
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2012.02.003