Entanglement entropy in critical phenomena and analog models of quantum gravity

Abstract There are increasing evidences that quantum information theory has come to play a fundamental role in quantum gravity especially the holography. In this paper, we show some new potential connections between holography and quantum information theory. Particularly, by utilizing the multiflow description of the holographic entanglement of purification (HEoP) defined in relative homology, we obtain several new inequalities of HEoP under a max multiflow configuration. Each inequality derived for HEoP has a corresponding inequality of the holographic entanglement entropy (HEE). This is further confirmed by geometric analysis. In addition, we conjecture that, based on flow considerations, each property of HEE that can be derived from bit threads may have a corresponding property for HEoP that can be derived from bit threads defined in relative homology.

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Comment on Coleman-DeLuccia instantons

SciPost Physics ◽

10.21468/scipostphys.12.1.015 ◽

2022 ◽

Vol 12 (1) ◽

Author(s):

Thomas Banks ◽

Bingnan Zhang

Keyword(s):

Models Of Quantum Gravity ◽

Quantum Gravity ◽

Transition Probabilities ◽

Detailed Balance ◽

De Sitter Space ◽

Positive Energy ◽

De Sitter ◽

Finite Area ◽

Quantum Models

We complete an old argument that causal diamonds in the crunching region of the Lorentzian continuation of a Coleman-Deluccia instanton for transitions out of de Sitter space have finite area, and provide quantum models consistent with the principle of detailed balance, which can mimic the instanton transition probabilities for the cases where this diamond is larger or smaller than the causal patch of de Sitter space. We review arguments that potentials which do not have a positive energy theorem when the lowest de Sitter minimum is shifted to zero, may not correspond to real models of quantum gravity.

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Entanglement entropy of physical states in hypercuboidally truncated spin foam quantum gravity

Classical and Quantum Gravity ◽

10.1088/1361-6382/ab77ea ◽

2020 ◽

Vol 37 (9) ◽

pp. 094001

Author(s):

Benjamin Bahr

Keyword(s):

Quantum Gravity ◽

Entanglement Entropy ◽

Spin Foam

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One-loop renormalization in quantum gravity

Introduction to Quantum Field Theory with Applications to Quantum Gravity ◽

10.1093/oso/9780198838319.003.0020 ◽

2021 ◽

pp. 474-487

Author(s):

Iosif L. Buchbinder ◽

Ilya L. Shapiro

Keyword(s):

General Relativity ◽

Models Of Quantum Gravity ◽

Quantum Gravity ◽

Detailed Analysis ◽

Polynomial Model ◽

Similar Calculation ◽

Higher Derivative ◽

Gauge Fixing ◽

Fourth Derivative ◽

Detailed Derivation

This chapter demonstrates the basic methods of one-loop calculations in quantum gravity. Basing its discussion on the general results obtained in chapter 10, it first presents a detailed analysis of the gauge-fixing dependence of one-loop divergences in quantum general relativity and higher-derivative models of quantum gravity. After that, a detailed derivation of divergences in quantum general relativity is given, with the simplest parametrization of the quantum metric and minimal gauge fixing. One-loop divergences in the general (non-conformal) fourth-derivative quantum gravity are then derived in less detail. For a similar calculation in the superrenormalizable polynomial model (superrenormalizable gravity), the chapter just presents and discusses the final result.

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Entanglement entropy in loop quantum gravity

Physical Review D ◽

10.1103/physrevd.77.104006 ◽

2008 ◽

Vol 77 (10) ◽

Cited By ~ 34

Author(s):

William Donnelly

Keyword(s):

Quantum Gravity ◽

Loop Quantum Gravity ◽

Entanglement Entropy

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GRAVITY AS BF THEORY PLUS POTENTIAL

International Journal of Modern Physics A ◽

10.1142/s0217751x09046151 ◽

2009 ◽

Vol 24 (15) ◽

pp. 2776-2782 ◽

Cited By ~ 12

Author(s):

KIRILL KRASNOV

Keyword(s):

General Relativity ◽

Models Of Quantum Gravity ◽

Quantum Gravity ◽

Alternative Formulation ◽

Potential Term ◽

Bf Theory ◽

Spin Foam Models ◽

Spin Foam ◽

To Come

Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the potential is taken to be infinitely steep one recovers general relativity. For a generic potential the theory still describes gravity in that it propagates just two graviton polarizations. The arising class of theories is of the type amenable to spin foam quantization methods, and, we argue, may allow one to come to terms with renormalization in the spin foam context.

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