10 D Euclidean dynamical triangulations

TL;DR

This study numerically explores 10-dimensional Euclidean quantum gravity using dynamical triangulations, revealing phase behaviors similar to lower dimensions and a natural branched polymer state when the Einstein-Hilbert action is absent.

Contribution

It extends dynamical triangulation methods to 10 dimensions, identifying phase structures and natural states in high-dimensional quantum gravity.

Findings

Two phases observed, similar to lower-dimensional models.

The natural state without Einstein-Hilbert action resembles branched polymers.

Behavior of phases aligns with known lower-dimensional quantum gravity models.

Abstract

We investigate numerically 10 - dimensional Euclidean quantum gravity (with discretized Einstein - Hilbert action) in the framework of the dynamical triangulation approach. For the considered values of the gravitational coupling we observed two phases, the behavior of which is found to be similar to that of the crumpled and elongated phases of 3, 4 and 5 dimensional models. Surprisingly, (for the observed lattice sizes) the natural state of the 10 D system (when the Einstein - Hilbert action is turned off) is found to resemble branched polymer while in the low dimensional systems the natural state belongs to the crumpled phase.