Gravitational Actions in Two Dimensions and the Mabuchi Functional
arXiv:1112.1352 · doi:10.1016/j.nuclphysb.2012.02.003
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.
34 pages; v2: missing log in eq. (3.26) added