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 analyse this theory using the minisuperspace method (quantum mechanics of the zero mode). In this approximation we show that the associated Hamiltonian coincides with the (quantum mechanical) Liouville Hamiltonian. As a consequence both theories share the same spectrum, eigenfunctions and - in this approximation - correlation functions.