scholarly journals Universal critical behavior in tensor models for four-dimensional quantum gravity

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Astrid Eichhorn ◽  
Johannes Lumma ◽  
Antonio D. Pereira ◽  
Arslan Sikandar
Keyword(s):  
Quantum Gravity ◽  
Critical Behavior ◽  
Tensor Models

scholarly journals FRG analysis of a multi-matrix model for 3d Lorentzian quantum gravity

2020 ◽  
Author(s):  
Andreas G. A. Pithis ◽  
Antonio Duarte Pereira ◽  
Astrid Eichhorn
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Recent Progress ◽  
Gravity Models ◽  
Group Method ◽  
Critical Properties ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
Tensor Models ◽  
Practical Tool

At criticality, discrete quantum gravity models are expected to give rise to continuum spacetime. Recent progress has established the functional Renormalization Group method in the context of such models as a practical tool to study their critical properties and to chart their phase diagrams. Here, we apply these techniques to the multi-matrix model with ABAB-interaction potentially relevant for Lorentzian quantum gravity in 3 dimensions. We characterize the fixed-point structure and phase diagram of this model, paving the way for functional RG studies of more general multi-matrix or tensor models encoding causality.

scholarly journals Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 53 ◽  
Author(s):  
Astrid Eichhorn ◽  
Tim Koslowski ◽  
Antonio Pereira
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Continuum Limit ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Discrete Models ◽  
Practical Implementation ◽  
Tensor Model ◽  
Independent Form ◽  
Tensor Models

A background-independent route towards a universal continuum limit in discrete models of quantum gravity proceeds through a background-independent form of coarse graining. This review provides a pedagogical introduction to the conceptual ideas underlying the use of the number of degrees of freedom as a scale for a Renormalization Group flow. We focus on tensor models, for which we explain how the tensor size serves as the scale for a background-independent coarse-graining flow. This flow provides a new probe of a universal continuum limit in tensor models. We review the development and setup of this tool and summarize results in the two- and three-dimensional case. Moreover, we provide a step-by-step guide to the practical implementation of these ideas and tools by deriving the flow of couplings in a rank-4-tensor model. We discuss the phenomenon of dimensional reduction in these models and find tentative first hints for an interacting fixed point with potential relevance for the continuum limit in four-dimensional quantum gravity.

scholarly journals TENSOR MODELS AND HIERARCHY OF n-ARY ALGEBRAS

2011 ◽  
Vol 26 (19) ◽  
pp. 3249-3258 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Algebraic Structure ◽  
The Other ◽  
Invariant Form ◽  
Infinitesimal Symmetry ◽  
Tensor Models ◽  
Symmetry Transformations

Tensor models are generalization of matrix models, and are studied as models of quantum gravity. It is shown that the symmetry of the rank-three tensor models is generated by a hierarchy of n-ary algebras starting from the usual commutator, and the 3-ary algebra symmetry reported in the previous paper is just a single sector of the whole structure. The condition for the Leibnitz rules of the n-ary algebras is discussed from the perspective of the invariance of the underlying algebra under the n-ary transformations. It is shown that the n-ary transformations which keep the underlying algebraic structure invariant form closed finite n-ary Lie subalgebras. It is also shown that, in physical settings, the 3-ary transformation practically generates only local infinitesimal symmetry transformations, and the other more nonlocal infinitesimal symmetry transformations of the tensor models are generated by higher n-ary transformations.

MULTICRITICALITY IN STABILIZED 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (37) ◽  
pp. 3465-3477
Author(s):  
OSCAR DIEGO ◽  
JOSÉ GONZÁLEZ
Keyword(s):  
Phase Diagram ◽  
Quantum Gravity ◽  
Critical Behavior ◽  
Critical Line ◽  
Tricritical Point ◽  
Stable Phase ◽  
Multicritical Point ◽  
Stochastic Stabilization ◽  
The Matrix ◽  
Pure Gravity

We study the simplest perturbation of the matrix model for pure gravity susceptible of reaching the k=3 multicritical point in the framework of the stochastic stabilization of 2D quantum gravity. We show the existence of a line of points in the phase diagram with the genuine critical behavior of the k=2 theory. All the points of the critical line, up to the tricritical point, can be approached from a stable phase at the dominant level in 1/N expansion.

Critical behavior of the nonperturbative stabilization of 2D quantum gravity

1991 ◽  
Vol 258 (1-2) ◽  
pp. 55-60 ◽  
Author(s):  
J González ◽  
M.A.H Vozmediano
Keyword(s):  
Quantum Gravity ◽  
Critical Behavior

scholarly journals A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

2010 ◽  
Vol 25 (23) ◽  
pp. 4475-4492 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
General Relativity ◽  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Dynamical Variable ◽  
Renormalization Procedure ◽  
Emergent Phenomena ◽  
Tensor Models ◽  
Theories Of Gravity

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parametrized by a scalar and a symmetric two-tensor, it is argued that, in general situations, the infrared dynamics of the tensor models should be described by scalar-tensor theories of gravity.

scholarly journals THE WEINGARTEN MODEL À LA POLYAKOV

1992 ◽  
Vol 07 (18) ◽  
pp. 1651-1660 ◽  
Author(s):  
SIMON DALLEY
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Critical Behavior ◽  
Continuum Limit ◽  
Hermitian Matrix ◽  
Gauge Model ◽  
Vertex Models ◽  
Lattice Gauge ◽  
Genus Expansion ◽  
The Continuum

The Weingarten lattice gauge model of Nambu-Goto strings is generalized to allow for fluctuations of an intrinsic worldsheet metric through a dynamical quadrilation. The continuum limit is taken for c≤1 matter, reproducing the results of Hermitian matrix models to all orders in the genus expansion. For the compact c=1 case the vortices are Wilson lines, whose exclusion leads to the theory of non-interacting fermions. As a by-product of the analysis one finds the critical behavior of SOS and vertex models coupled to 2D quantum gravity.

scholarly journals The phase diagram of the multi-matrix model with ABAB interaction from functional renormalization

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Astrid Eichhorn ◽  
Antonio D. Pereira ◽  
Andreas G. A. Pithis
Keyword(s):  
Phase Diagram ◽  
Quantum Gravity ◽  
Matrix Model ◽  
Gravity Models ◽  
Group Method ◽  
Critical Properties ◽  
Renormalization Group Method ◽  
Functional Renormalization Group ◽  
Tensor Models ◽  
Practical Tool

Abstract At criticality, discrete quantum-gravity models are expected to give rise to continuum spacetime. Recent progress has established the functional renormalization group method in the context of such models as a practical tool to study their critical properties and to chart their phase diagrams. Here, we apply these techniques to the multi-matrix model with ABAB interaction potentially relevant for Lorentzian quantum gravity in 3 dimensions. We characterize the fixed-point structure and phase diagram of this model, paving the way for functional RG studies of more general multi-matrix or tensor models encoding causality and subjecting the technique to another strong test of its performance in discrete quantum gravity by comparing to known results.

scholarly journals Thermodynamics of BTZ black holes in gravity’s rainbow

2017 ◽  
Vol 32 (15) ◽  
pp. 1750076 ◽  
Author(s):  
Salwa Alsaleh
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Free Energy ◽  
Quantum Gravity ◽  
Critical Behavior ◽  
Loop Quantum Gravity ◽  
Temperature Deformation ◽  
Btz Black Hole ◽  
Gravity’S Rainbow ◽  
Gravity's Rainbow

In this paper, we deform the thermodynamics of a BTZ black hole from rainbow functions in gravity’s rainbow. The rainbow functions will be motivated from the results in loop quantum gravity and noncommutative geometry. It will be observed that the thermodynamics gets deformed due to these rainbow functions, indicating the existence of a remnant. However, the Gibbs free energy does not get deformed due to these rainbow functions, and so the critical behavior from Gibbs does not change by this deformation. This is because the deformation in the entropy cancels out the temperature deformation.

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