Simulations of Discrete Random Geometries: Simplicial Quantum Gravity and Quantum String Theory

TL;DR

This paper explores two discrete models of random geometries, showing how matter fields alter phase structures in quantum gravity and demonstrating divergence elimination in supersymmetric string discretizations, with numerical confirmation of emergent structures.

Contribution

It introduces a strong coupling expansion technique to analyze phase changes in 4D simplicial quantum gravity with matter fields and investigates divergence issues in discretized superstring models.

Findings

Matter gauge fields change phase structure in 4D quantum gravity.

Divergences are eliminated in discretized supersymmetric string models.

Large system extents show one-dimensional structures with power-law link length distributions.

Abstract

I investigate two discrete models of random geometries, namely simplicial quantum gravity and quantum string theory. In four-dimensional simplicial quantum gravity, I show that the addition of matter gauge fields to the model is capable of changing its phase structure by replacing the branched polymers of the pure gravity model with a new phase that has a negative string susceptibility exponent and a fractal dimension of four. Some of the results are derived from a strong coupling expansion of the model, a technique which is used here for the first time in this context. In quantum string theory, I study a discrete version of the IIB superstring. I show that the divergences encountered in the discretization of the bosonic string are eliminated in the supersymmetric case. I give theoretical arguments for the appearance of one-dimensional structures in the region of large system extents that manifest as a power-law tail in the link length distribution; this is confirmed by numerical simulations of the model. I also examine a lower-dimensional version of the IKKT matrix model, in which a similar effect can be observed.