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, Chopin

AU - Yu, Hoi Lai

N1 - Funding Information:
The research for this work has been supported by funds from the National Science Council of Taiwan under Grant Nos. NSC93-2112-M-006-011 and NSC94-2112-M-006-006; and the National Center for Theoretical Sciences. Y.L. was supported by NSFC (Nos. 10405027, 10205002) and SRF for ROCS, SEM.

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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U2 - 10.1016/j.physletb.2006.04.028

DO - 10.1016/j.physletb.2006.04.028

M3 - Article

AN - SCOPUS:33646369362

SN - 0370-2693

VL - 637

SP - 12

EP - 15

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 1-2

ER -