Causal Dynamical Triangulations in the Spincube Model of Quantum Gravity

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.

v4: published version; 18 pages

References in corpus (6)

• LQG vertex with finite Immirzi parameter
• Nonperturbative Quantum Gravity
• A New Spin Foam Model for 4d Gravity
• Topological Higher Gauge Theory - from BF to BFCG theory
• Spin-cube Models of Quantum Gravity
• A 2-categorical state sum model

Cited by in corpus (7)

• Effective Spin Foam Models for Four-Dimensional Quantum Gravity
• Effective Spin Foam Models for Lorentzian Quantum Gravity
• Discrete gravity dynamics from effective spin foams
• Higher Gauge Theories Based on 3-groups
• Nakanishi-Kugo-Ojima quantization of general relativity in Heisenberg picture
• Gauge protected entanglement between gravity and matter
• Construction and examples of higher gauge theories