Recent progress in the theory of random surfaces and simplicial quantum gravity

Alternative approaches to the study of the quantum gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages the introduction of particles and fields, while other approaches assume that spacetime should only be an emergent entity. We here argue that recent progress in the covariant formulation of quantum mechanics, suggests that empty spacetime is not physically meaningful. We illustrate our general thesis in the specific context of the noncommutative Snyder spacetime, which is also of some intrinsic interest, since hundreds of studies were devoted to its analysis. We show that empty Snyder spacetime, described in terms of a suitable kinematical Hilbert space, is discrete, but this is only a formal artifact: the discreteness leaves no trace on the observable properties of particles on the physical Hilbert space.

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

10.14293/s2199-1006.1.sor-.pp53mpx.v1 ◽

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.

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Random Surfaces and Liouville Quantum Gravity

Notices of the American Mathematical Society ◽

10.1090/noti2059 ◽

2020 ◽

Vol 67 (04) ◽

pp. 1

Author(s):

Ewain Gwynne

Keyword(s):

Quantum Gravity ◽

Random Surfaces

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Quantum gravity and random surfaces

Nuclear Physics B - Proceedings Supplements ◽

10.1016/0920-5632(92)90231-g ◽

1992 ◽

Vol 26 ◽

pp. 93-110 ◽

Cited By ~ 8

Author(s):

H. Kawai

Keyword(s):

Quantum Gravity ◽

Random Surfaces

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INTERACTION HIERARCHY: STRING AND QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732396001399 ◽

1996 ◽

Vol 11 (17) ◽

pp. 1379-1396 ◽

Cited By ~ 24

Author(s):

G.K. SAVVIDY ◽

K.G. SAVVIDY

Keyword(s):

Partition Function ◽

Quantum Gravity ◽

Spin System ◽

Scaling Limit ◽

Functional Integral ◽

Local Interaction ◽

Linear Action ◽

Random Surfaces

We have found that the functional integral for quantum gravity can be represented as a superposition of less complicated theory of random surfaces with Euler character as an action. We propose an alternative linear action A(M4) for quantum gravity. On the lattice we constructed spin system with local interaction, which has the equivalent partition function. The scaling limit is discussed.

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FRACTAL STRUCTURE OF 2d—QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732388000982 ◽

1988 ◽

Vol 03 (08) ◽

pp. 819-826 ◽

Cited By ~ 974

Author(s):

V.G. KNIZHNIK ◽

A.M. POLYAKOV ◽

A.B. ZAMOLODCHIKOV

Keyword(s):

Quantum Gravity ◽

Fractal Structure ◽

Numerical Analyses ◽

Complete Agreement ◽

Random Surfaces ◽

Anomalous Dimensions ◽

Explicit Formulae

We resolve renormalization problems, indicated in Ref. 1 and find explicit formulae for the spectrum of anomalous dimensions in 2d—quantum gravity. Comparison with combinatorial approximation of random surfaces and its numerical analyses shows complete agreement with all known facts.

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