Mabuchi spectrum from the minisuperspace

Abstract

It was recently shown that other functionals contribute to the effective action for the Liouville field when considering massive matter coupled to two-dimensional gravity in the conformal gauge. The most important of these new contributions corresponds to the Mabuchi functional. We propose a minisuperspace action that reproduces the main features of the Mabuchi action in order to describe the dynamics of the zero-mode. We show that the associated Hamiltonian coincides with the (quantum mechanical) Liouville Hamiltonian. As a consequence the Liouville theory and our model of the Mabuchi theory both share the same spectrum, eigenfunctions and - in this approximation - correlation functions.

4 pages; v2: change presentation but conclusion unchanged, match published version

References in corpus (2)

• FQHE on curved backgrounds, free fields and large N
• Notes on Liouville Theory at c<=1

Cited by in corpus (6)

• 2D gravitational Mabuchi action on Riemann surfaces with boundaries
• BRST cohomology of timelike Liouville theory
• Minisuperspace computation of the Mabuchi spectrum
• Integrable higher-dimensional cosmology with separable variables in an Einstein-dilaton-antisymmetric field theory
• Gravitational action for a massive Majorana fermion in 2d quantum gravity
• A short note on dynamics and degrees of freedom in $2d$ classical gravity