# Minisuperspace computation of the Mabuchi spectrum

## TL;DR

This paper explores the quantum properties of the Mabuchi functional in 2D gravity, showing its spectrum matches Liouville theory in a simplified minisuperspace model, supporting the conjecture of their equivalence.

## Contribution

It introduces a minisuperspace model for the Mabuchi functional and demonstrates its Hamiltonian coincides with Liouville theory, suggesting their spectra are identical.

## Key findings

- Hamiltonian of Mabuchi theory equals Liouville Hamiltonian
- Spectrum and correlation functions match in minisuperspace approximation
- Supports conjecture of Mabuchi and Liouville equivalence in 2D gravity

## Abstract

It was shown recently that, beside the traditional Liouville action, other functionals appear in the gravitational action of two-dimensional quantum gravity in the conformal gauge, the most important one being the Mabuchi functional. In a letter we proposed a minisuperspace action for this theory and used it to perform its canonical quantization. We found that the Hamiltonian of the Mabuchi theory is equal to the one of the Liouville theory and thus that the spectrum and correlation functions match in this approximation. In this paper we provide motivations to support our conjecture.