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Towards self dual Loop Quantum Gravity Jibril Ben Achour

  1. Nov 27, 2015 #1
    interesting new paper on possible new research direction for LQG

    Towards self dual Loop Quantum Gravity
    Jibril Ben Achour
    (Submitted on 23 Nov 2015)
    In this PhD thesis, we introduced a new strategy to investigate the kinematical and physical predictions of self dual Loop Quantum Gravity (LQG) and by-passed the old problem of implementing quantum mechanically the so called reality conditions inherent to the self dual Ashtekar's phase space.
    We first review the loop quantization of the spherically isolated horizon and the computation of its micro-canonical entropy. Then we present the so called gas of punctures model for the quantum horizon, discussing its results in the canonical and grand-canonical ensembles and its limits.
    The fourth chapter is devoted to studying to what extend the loop quantization based on the self dual variables could cure those problems. We introduce a new strategy, based on an analytic continuation of the degeneracy from γ∈R to γ=±i. We review in details the construction of the procedure, and present the results. At the leading term, we recover exactly the Bekenstein-Hawking area law.
    The fifth chapter is devoted to understanding more precisely the interplay between the status of the Immirzi parameter. In order to do this, we introduce from a new toy model describing 2+1 gravity which depends explicitly on the Immirzi parameter.
    Finally, the sixth chapter is devoted to applying our procedure to the simplest Loop Quantum Cosmology model. By first constructing the LQC dynamics for any arbitrary spin j and then implementing our analytic continuation, we show that our procedure preserves the key features of the LQC models, i.e. we obtain a bouncing universe which admits the right semi classical limit after the bounce.
    PhD Thesis - 254 pages

    worth remembering since the paper is about self-dual LQG
  2. jcsd
  3. Nov 27, 2015 #2


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    Last edited: Nov 27, 2015
  4. Nov 27, 2015 #3
    good idea there marcus. when LQG when y= i it is self-dual. what are the benefits of making LQG self-dual
  5. Nov 27, 2015 #4


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    It seems to be related to the line of work which tries to make Immizi imaginary. Originally the thinking was the Immirzi should be set to match the Hawking formula? But I think some more recent thinking on LQG black holes has imaginary Immirzi.

    Eg. slide 17 of http://www.ihes.fr/~vanhove/Slides/NOUI-IHES-novembre2013.pdf

    From Ben Achour's thesis in the OP (p79):
    "Going further in our interpretation, the Immirzi parameter could be regarded as a kind of regulator, allowing to Wick rotate the kinematical quantum theory. At the end of the quantization procedure, should be sent to the purely imaginary value, in order to recover to self dual quantum theory. This is the point of view adopted in this manuscript."
    Last edited: Nov 27, 2015
  6. Nov 27, 2015 #5
    i recall Steve Carlip had a paper on that as well. his thesis is y = i results in better semiclassical black hole entropy calculation.

    worth noting that the original kodama wave function y = i
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