scholarly journals CDT Quantum Toroidal Spacetimes: An Overview

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 79
Author(s):  
Jan Ambjorn ◽  
Zbigniew Drogosz ◽  
Jakub Gizbert-Studnicki ◽  
Andrzej Görlich ◽  
Jerzy Jurkiewicz ◽  
...  
Keyword(s):  
Lattice Theory ◽  
Continuum Limit ◽  
Fractal Structure ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Quantum Geometry ◽  
Special Boundary ◽  
Dramatic Effect ◽  
Causal Dynamical Triangulations ◽  
Dynamical Triangulations

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.

scholarly journals The spectral dimension in 2D CDT gravity coupled to scalar fields

2015 ◽  
Vol 30 (13) ◽  
pp. 1550077 ◽  
Author(s):  
J. Ambjørn ◽  
A. Görlich ◽  
J. Jurkiewicz ◽  
H. Zhang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Spectral Dimension ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Two Dimensional ◽  
Imaginary Time ◽  
Causal Dynamical Triangulations ◽  
Pure Gravity ◽  
Dynamical Triangulations

Causal Dynamical Triangulations (CDT) provide a non-perturbative formulation of Quantum Gravity assuming the existence of a global time foliation. In our earlier study we analyzed the effect of including d copies of a massless scalar field in the two-dimensional CDT model with imaginary time. For d > 1 we observed the formation of a "blob", somewhat similar to that observed in four-dimensional CDT without matter. In the two-dimensional case the "blob" has a Hausdorff dimension DH = 3. In this paper, we study the spectral dimension DS of the two-dimensional CDT-universe, both for d = 0 (pure gravity) and d = 4. We show that in both cases the spectral dimension is consistent with DS = 2.

scholarly journals Scalar fields in causal dynamical triangulations

2021 ◽  
Author(s):  
Jan Ambjorn ◽  
Zbigniew Drogosz ◽  
Jakub Gizbert-Studnicki ◽  
Andrzej Görlich ◽  
Jerzy Jurkiewicz ◽  
...  
Keyword(s):  
Scalar Fields ◽  
Causal Dynamical Triangulations ◽  
Dynamical Triangulations

scholarly journals How round is the quantum de Sitter universe?

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
N. Klitgaard ◽  
R. Loll
Keyword(s):  
Quantum Dynamics ◽  
Global Scale ◽  
Quantum Geometry ◽  
De Sitter ◽  
Curved Space ◽  
Causal Dynamical Triangulations ◽  
Quantum Universe ◽  
Local Properties ◽  
Dynamical Triangulations ◽  
De Sitter Universe

AbstractWe investigate the quantum Ricci curvature, which was introduced in earlier work, in full, four-dimensional quantum gravity, formulated nonperturbatively in terms of Causal Dynamical Triangulations (CDT). A key finding of the CDT approach is the emergence of a universe of de Sitter-type, as evidenced by the successful matching of Monte Carlo measurements of the quantum dynamics of the global scale factor with a semiclassical minisuperspace model. An important question is whether the quantum universe exhibits semiclassicality also with regard to its more local geometric properties. Using the new quantum curvature observable, we examine whether the (quasi-)local properties of the quantum geometry resemble those of a constantly curved space. We find evidence that on sufficiently large scales the curvature behaviour is compatible with that of a four-sphere, thus strengthening the interpretation of the dynamically generated quantum universe in terms of a de Sitter space.

scholarly journals Impact of topology in causal dynamical triangulations quantum gravity

2016 ◽  
Vol 94 (4) ◽  
Author(s):  
J. Ambjørn ◽  
Z. Drogosz ◽  
J. Gizbert-Studnicki ◽  
A. Görlich ◽  
J. Jurkiewicz ◽  
...  
Keyword(s):  
Quantum Gravity ◽  
Causal Dynamical Triangulations ◽  
Dynamical Triangulations

scholarly journals New higher-order transition in causal dynamical triangulations

2017 ◽  
Vol 95 (12) ◽  
Author(s):  
J. Ambjorn ◽  
D. Coumbe ◽  
J. Gizbert-Studnicki ◽  
A. Görlich ◽  
J. Jurkiewicz
Keyword(s):  
Higher Order ◽  
Order Transition ◽  
Causal Dynamical Triangulations ◽  
Dynamical Triangulations

CHIRALLY EXTENDED QUANTUM CHROMODYNAMICS

1995 ◽  
Vol 06 (05) ◽  
pp. 725-742 ◽  
Author(s):  
RICHARD C. BROWER ◽  
YUE SHEN ◽  
CHUNG-I TAN
Keyword(s):  
Quantum Chromodynamics ◽  
Quark Mass ◽  
Continuum Limit ◽  
Chiral Limit ◽  
Scalar Fields ◽  
Weak Coupling Limit ◽  
Slowing Down ◽  
Large N ◽  
Chiral Invariance ◽  
The Continuum

We propose an extended Quantum Chromodynamics (XQCD) Lagrangian in which the fermions are coupled to elementary scalar fields through a Yukawa coupling which preserves chiral invariance. Our principle motivation is to find a new lattice formulation for QCD which avoids the source of critical slowing down usually encountered as the bare quark mass is tuned to the chiral limit. The phase diagram and the weak coupling limit for XQCD are studied. They suggest a conjecture that the continuum limit of XQCD is the same as the continuum limit of conventional lattice formulation of QCD. As examples of such universality, we present the large N solutions of two prototype models for XQCD, in which the mass of the spurious pion and sigma resonance go to infinity with the cut-off. Even if the universality conjecture turns out to be false, we believe that XQCD will still be useful as a low energy effective action for QCD phenomenology on the lattice. Numerical simulations are recommended to further investigate the possible benefits of XQCD in extracting QCD predictions.

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