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Review

CDT Quantum Toroidal Spacetimes: An Overview

1
The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
2
Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
3
Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, PL 30-348 Kraków, Poland
*
Author to whom correspondence should be addressed.
Academic Editor: Włodzimierz Piechocki
Universe 2021, 7(4), 79; https://doi.org/10.3390/universe7040079
Received: 28 February 2021 / Revised: 19 March 2021 / Accepted: 21 March 2021 / Published: 26 March 2021
(This article belongs to the Special Issue Gravitational Singularities and Their Quantum Fates)
Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is coordinate-independent in the spatial directions. The higher-order phase transitions observed in the model may be used to define a continuum limit of the lattice theory. Some aspects of the transitions are better studied when the topology of space is toroidal rather than spherical. In addition, a toroidal spatial topology allows us to understand more easily the nature of typical quantum fluctuations of the geometry. In particular, this topology makes it possible to use massless scalar fields that are solutions to Laplace’s equation with special boundary conditions as coordinates that capture the fractal structure of the quantum geometry. When such scalar fields are included as dynamical fields in the path integral, they can have a dramatic effect on the geometry. View Full-Text
Keywords: quantum gravity; lattice quantum field theory; dynamical triangulations; emergent spacetime quantum gravity; lattice quantum field theory; dynamical triangulations; emergent spacetime
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MDPI and ACS Style

Ambjorn, J.; Drogosz, Z.; Gizbert-Studnicki, J.; Görlich, A.; Jurkiewicz, J.; Németh, D. CDT Quantum Toroidal Spacetimes: An Overview. Universe 2021, 7, 79. https://doi.org/10.3390/universe7040079

AMA Style

Ambjorn J, Drogosz Z, Gizbert-Studnicki J, Görlich A, Jurkiewicz J, Németh D. CDT Quantum Toroidal Spacetimes: An Overview. Universe. 2021; 7(4):79. https://doi.org/10.3390/universe7040079

Chicago/Turabian Style

Ambjorn, Jan, Zbigniew Drogosz, Jakub Gizbert-Studnicki, Andrzej Görlich, Jerzy Jurkiewicz, and Dániel Németh. 2021. "CDT Quantum Toroidal Spacetimes: An Overview" Universe 7, no. 4: 79. https://doi.org/10.3390/universe7040079

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