Effective gauge group of pure loop quantum gravity is SO ( 3 )

New estimate of the Immirzi parameter

Chung-Hsien Chou, Yi Ling, Cho-Pin Soo, Hoi Lai Yu

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3 Citations (Scopus)

Abstract

We argue that the effective gauge group for pure four-dimensional loop quantum gravity (LQG) is SO ( 3 ) (or SO ( 3, C )) instead of SU ( 2 ) (or SL ( 2, C )). As a result, links with half-integer spins in spin network states are not realized for pure LQG, implying a modification of the spectra of area and volume operators. Our observations imply a new value of γ ≈ 0.170 for the Immirzi parameter which is obtained from matching the Bekenstein-Hawking entropy to the number of states from LQG calculations. Moreover, even if the dominant contribution to the entropy is not assumed to come from configurations with the minimum spins, the results of both pure LQG and the supersymmetric extension of LQG can be made compatible when only integer spins are realized for the former, while the latter also contains half-integer spins, together with an Immirzi parameter for the supersymmetric case which is twice the value of the SO ( 3 ) theory. We also verify that the - frac(1, 2) coefficient of logarithmic correction to the Bekenstein-Hawking entropy formula is robust, independent of whether only integer, or also half-integer spins, are realized.

Original languageEnglish
Pages (from-to)12-15
Number of pages4
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume637
Issue number1-2
DOIs
Publication statusPublished - 2006 Jun 1

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integers
gravitation
estimates
entropy
operators
coefficients
configurations

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Cite this

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title = "Effective gauge group of pure loop quantum gravity is SO ( 3 ): New estimate of the Immirzi parameter",
abstract = "We argue that the effective gauge group for pure four-dimensional loop quantum gravity (LQG) is SO ( 3 ) (or SO ( 3, C )) instead of SU ( 2 ) (or SL ( 2, C )). As a result, links with half-integer spins in spin network states are not realized for pure LQG, implying a modification of the spectra of area and volume operators. Our observations imply a new value of γ ≈ 0.170 for the Immirzi parameter which is obtained from matching the Bekenstein-Hawking entropy to the number of states from LQG calculations. Moreover, even if the dominant contribution to the entropy is not assumed to come from configurations with the minimum spins, the results of both pure LQG and the supersymmetric extension of LQG can be made compatible when only integer spins are realized for the former, while the latter also contains half-integer spins, together with an Immirzi parameter for the supersymmetric case which is twice the value of the SO ( 3 ) theory. We also verify that the - frac(1, 2) coefficient of logarithmic correction to the Bekenstein-Hawking entropy formula is robust, independent of whether only integer, or also half-integer spins, are realized.",
author = "Chung-Hsien Chou and Yi Ling and Cho-Pin Soo and Yu, {Hoi Lai}",
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TY - JOUR

T1 - Effective gauge group of pure loop quantum gravity is SO ( 3 )

T2 - New estimate of the Immirzi parameter

AU - Chou, Chung-Hsien

AU - Ling, Yi

AU - Soo, Cho-Pin

AU - Yu, Hoi Lai

PY - 2006/6/1

Y1 - 2006/6/1

N2 - We argue that the effective gauge group for pure four-dimensional loop quantum gravity (LQG) is SO ( 3 ) (or SO ( 3, C )) instead of SU ( 2 ) (or SL ( 2, C )). As a result, links with half-integer spins in spin network states are not realized for pure LQG, implying a modification of the spectra of area and volume operators. Our observations imply a new value of γ ≈ 0.170 for the Immirzi parameter which is obtained from matching the Bekenstein-Hawking entropy to the number of states from LQG calculations. Moreover, even if the dominant contribution to the entropy is not assumed to come from configurations with the minimum spins, the results of both pure LQG and the supersymmetric extension of LQG can be made compatible when only integer spins are realized for the former, while the latter also contains half-integer spins, together with an Immirzi parameter for the supersymmetric case which is twice the value of the SO ( 3 ) theory. We also verify that the - frac(1, 2) coefficient of logarithmic correction to the Bekenstein-Hawking entropy formula is robust, independent of whether only integer, or also half-integer spins, are realized.

AB - We argue that the effective gauge group for pure four-dimensional loop quantum gravity (LQG) is SO ( 3 ) (or SO ( 3, C )) instead of SU ( 2 ) (or SL ( 2, C )). As a result, links with half-integer spins in spin network states are not realized for pure LQG, implying a modification of the spectra of area and volume operators. Our observations imply a new value of γ ≈ 0.170 for the Immirzi parameter which is obtained from matching the Bekenstein-Hawking entropy to the number of states from LQG calculations. Moreover, even if the dominant contribution to the entropy is not assumed to come from configurations with the minimum spins, the results of both pure LQG and the supersymmetric extension of LQG can be made compatible when only integer spins are realized for the former, while the latter also contains half-integer spins, together with an Immirzi parameter for the supersymmetric case which is twice the value of the SO ( 3 ) theory. We also verify that the - frac(1, 2) coefficient of logarithmic correction to the Bekenstein-Hawking entropy formula is robust, independent of whether only integer, or also half-integer spins, are realized.

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