Quantum properties of the polytopic action in some simple geometries

TL;DR

This paper computes the partition function for a new 'polytopic' gravitational action in simple 2D geometries, analyzing its dependence on key parameters and comparing with existing quantum gravity results.

Contribution

It introduces and evaluates the partition function for the polytopic action in basic 2D geometries, providing insights into its quantum properties.

Findings

Partition function computed for genus zero and one geometries.

Dependence on coupling and cosmological constants analyzed.

Comparison with standard 2D quantum gravity scaling results.

Abstract

The partition function corresponding to the "polytopic" action, a new action for the gravitational interaction which we have proposed recently, is computed in the simplest two-dimensional geometries of genus zero and one. The functional integral over the Liouville field is approximated by an ordinary integral over the constant zero mode. We study the dependence on both the coupling constant and the cosmological constant, and compare with recent scaling results in standard 2D quantum gravity.