Causal Dynamical Triangulations in the Spincube Model of Quantum Gravity

TL;DR

This paper explores the spincube model of quantum gravity, revealing that under certain constraints it can reproduce the causal dynamical triangulations (CDT) state sum, thus unifying two major approaches in the field.

Contribution

It demonstrates that the spincube model can encompass the CDT state sum as a special case, offering a unified framework for quantum gravity approaches.

Findings

The simplicity constraint leads to nearly identical 4-simplices in the triangulation.

The CDT state sum emerges as a special case within the spincube model.

The spincube model bridges properties of spinfoam and CDT approaches.

Abstract

We study the implications of the simplicity constraint in the spincube model of quantum gravity. By relating the edge-lengths to the integer areas of triangles, the simplicity constraint imposes very strong restrictions between them, ultimately leading to a requirement that all 4-simplices in the triangulation must be almost mutually identical. As a surprising and unexpected consequence of this property, one can obtain the CDT state sum as a special case of the spincube state sum. This relationship brings new insight into the long-standing problem of the relationship between the spinfoam approach and the CDT approach to quantum gravity. In particular, it turns out that the spincube model contains properties of both approaches, providing a single unifying framework for their analysis and comparison. In addition, the spincube state sum also contains some other special cases, very similar but not equivalent to the CDT state sum.