Gravitational Actions in Two Dimensions and the Mabuchi Functional
High Energy Physics - Theory
2012-03-13 v2 Mathematical Physics
math.MP
Abstract
The Mabuchi energy is an interesting geometric functional on the space of K\"ahler metrics that plays a crucial r\^ole in the study of the geometry of K\"ahler 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.
Keywords
Cite
@article{arxiv.1112.1352,
title = {Gravitational Actions in Two Dimensions and the Mabuchi Functional},
author = {Frank Ferrari and Semyon Klevtsov and Steve Zelditch},
journal= {arXiv preprint arXiv:1112.1352},
year = {2012}
}
Comments
34 pages; v2: missing log in eq. (3.26) added