Gravitational Actions in Two Dimensions and the Mabuchi Functional

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

References in corpus (3)

• Lectures on Stability and Constant Scalar Curvature
• Random Geometry, Quantum Gravity and the Kähler Potential
• A negative mass theorem for surfaces of positive genus

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