The Configuration Space of Conformal Connection-Dynamics

TL;DR

This paper demonstrates that the configuration space in conformal connection-dynamics generalizes the Teichmüller space concept, revealing that the Barbero-Immirzi parameter acts as a dilaton in conformal canonical gravity theories.

Contribution

It establishes that the configuration space of conformal connection-dynamics is a higher-dimensional Teichmüller space, extending previous results to non-Ricci flat metrics.

Findings

Configuration space is a higher-dimensional Teichmüller space.

Barbero-Immirzi parameter acts as a dilaton in conformal theories.

Results apply to non-Ricci flat metrics.

Abstract

The configuration space of the reduced Hamiltonian formulation of quantum gravity has been shown, for non-Ricci flat metrics, to be a higher-dimensional analogue of the Teichm\"{u}ller space of conformal structures on a Riemann surface. In this article we show that the configuration space of conformal connection-dynamics is naturally a higher-dimensional Teichm\"{u}ller space, subject to the same condition. An immediate consequence of this result is that the Barbero-Immirzi parameter of loop quantum gravity naturally assumes a dilatonic character in all conformal canonical gravity theories.