Gravitational Actions in Two Dimensions and the Mabuchi Functional

Details Gravitational Actions in Two Dimensions and the Mabuchi Functional Gravitational Actions in Two Dimensions and the Mabuchi Functional

2011-12-06

arxiv.org/abs/1112.1352v2

Nucl.Phys. B859 (2012) 341-369

Physics

High Energy Physics

High Energy Physics - Theory

34 pages; v2: missing log in eq. (3.26) added

Scientific paper

10.1016/j.nuclphysb.2012.02.003

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.

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