On gonihedric loops and quantum gravity

TL;DR

This paper analyzes the gonihedric loop model, a reformulation of a 2D spin model, using analytical height model mapping and matrix model techniques, concluding it has central charge zero and no continuous phase transition.

Contribution

It introduces a dual-method analysis of the gonihedric loop model, connecting lattice and gravitational perspectives, revealing its matter content and phase transition properties.

Findings

Model has central charge c=0 for all parameters

No continuous phase transition occurs in the model

Analytical and matrix model methods agree on the results

Abstract

We present an analysis of the gonihedric loop model, a reformulation of the two dimensional gonihedric spin model, using two different techniques. First, the usual regular lattice statistical physics problem is mapped onto a height model and studied analytically. Second, the gravitational version of this loop model is studied via matrix models techniques. Both methods lead to the conclusion that the model has $c_{matter}=0$ for all values of the parameters of the model. In this way it is possible to understand the absence of a continuous transition.