Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Four-Dimensional Entropy from Three-Dimensional Gravity

  1. Apr 24, 2015 #1
    http://arxiv.org/abs/1503.02981
    Four-Dimensional Entropy from Three-Dimensional Gravity
    S. Carlip
    (Submitted on 10 Mar 2015)
    At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1)-dimensional de Sitter space.
    8 pages
    ^

    is this paper applying ads/cft to LQG?
     
  2. jcsd
  3. Apr 24, 2015 #2

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Hi Kodama,
    Strictly speaking no. It does not apply any "Anti-deSitter/conformal field theory" theorem or conjecture to studying the LQG black hole.
    AdS/CFT is only one of a number of analytic strategies where information in the bulk (e.g. 4d) space is related to information on the boundary (e.g.3d) space.
    It's a highly publicized example of this but it is far from being the whole menu of bulk-boundary approaches.

    You picked a good author. Steve Carlip is a highly respected longtime expert. I've heard him talk when he gave an invited lecture at UC Berkeley on quantum gravity---the audience included a number of string theorists. He's quite familiar with AdS/CFT and would have said so clearly if he was using it.

    But he did not cite any of the main AdS/CFT papers and didn't invoke it, or even mention it in the main body of the paper. He made a brief mention of anti-deSitter at the end as something related that might be explored in future research.
    You know anti-deSitter basically means negative cosmological constant, and deSitter on the other hand means positive cosmological constant.
    As far as we can tell our universe is NOT anti-deSitter. It seems to have a positive cosmological constant.

    Carlip was using a kind of bulk-boundary approach that did not involve AdS/CFT. As I see it that makes his paper all the more innovative, more interesting, and more likely to be in line with the reality of nature. It's a fascinating paper and definitely worth discussing!
     
  4. Apr 24, 2015 #3

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Kodama, for me the thing about Carlip's paper is that he sets γ = i.
    He gets the BH area entropy law without complicating matters with a real Immirzi parameter. This is part of an exciting broader development--over the past year or two I've seen a number of LQG papers that use the original and natural Ashtekar variables without having to choose a real number for gamma. They are going back to the original self-dual formulation which uses the complex number i.

    Here's what Carlip says about it in the introduction to his paper. He makes it clear that setting γ = i and going through with the BH calculation is the essential thrust of the paper:
    ==quote==
    In the past few years, there have been intriguing hints that the entropy can also be obtained by setting γ = i [5–8]. This is the natural value: it makes the theory self-dual [9], and is the only choice for which the Ashtekar-Barbero-Sen connection (1.1) is a fully diffeomorphism-invariant spacetime connection [10,11]. Unfortunately, with this choice one must impose a reality conditions, a procedure that remains poorly defined. As a consequence, the theory with γ = i is not nearly as mathematically sophisticated as the version with real γ, and far fewer results have been established.

    In this paper, I will describe a simple new method for computing black hole entropy in loop quantum gravity with γ = i.
    ==endquote==

    This by itself makes this an important paper and also part of a significant recent trend in LQG.
     
  5. Apr 24, 2015 #4

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Two papers that are part of this development came out just this past quarter (Jan-March 2015) and are on the "most important paper" Poll:
    https://www.physicsforums.com/threa...rter-2015-mip-most-important-qg-paper.806409/

    http://arxiv.org/abs/1503.07855
    Loop quantum cosmology with self-dual variables
    Edward Wilson-Ewing
    (Submitted on 26 Mar 2015)
    Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular measure for the inner product in the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well-defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomy-like operators, some of which are well-defined; these operators in turn are used in the definition of a Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum dynamics are similar, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived, which provide a good approximation to the full quantum dynamics for sharply-peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a non-singular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.
    10 pages http://inspirehep.net/record/1356275

    http://arxiv.org/abs/1503.02981
    Four-Dimensional Entropy from Three-Dimensional Gravity
    S. Carlip
    (Submitted on 10 Mar 2015)
    At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1)-dimensional de Sitter space.
    8 pages http://inspirehep.net/record/1356275

    Carlip has an earlier paper on this same theme (developing the original self-dual Ashtekar variables in LQG, simply putting γ = i.)
    http://arxiv.org/abs/1410.5763
    A Note on Black Hole Entropy in Loop Quantum Gravity
    S. Carlip
    (Submitted on 21 Oct 2014 (v1), last revised 26 Mar 2015 (this version, v3))
    Several recent results have hinted that black hole thermodynamics in loop quantum gravity simplifies if one chooses an imaginary Barbero-Immirzi parameter γ=i. This suggests a connection with SL(2,ℂ) or SL(2,ℝ) conformal field theories at the "boundaries" formed by spin network edges intersecting the horizon. I present a bit of background regarding the relevant conformal field theories, along with some speculations about how they might be used to count black hole states. I show, in particular, that a set of unproven but plausible assumptions can lead to a boundary conformal field theory whose density of states matches the Bekenstein-Hawking entropy.
    13 pages.
     
    Last edited: Apr 24, 2015
  6. Apr 24, 2015 #5
    the kodama wave function also was forumlated as y = i.

    . "This is the natural value: it makes the theory self-dual [9], and is the only choice for which the Ashtekar-Barbero-Sen connection (1.1) is a fully diffeomorphism-invariant spacetime connection"

    for LQG to be a theory of QG doesn't y = i have to be the case for fully diffeomorphism-invariant spacetime connection"
     
  7. Apr 24, 2015 #6

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Good point! there's something happening here...
     
  8. Apr 24, 2015 #7
    y = i makes the theory self-dual.

    steve carlip's paper is stating that the entropy can arise regardless of y= real value is
     
  9. Apr 24, 2015 #8
    btw what are the implications for spinfoam if y = i?
     
  10. Apr 25, 2015 #9

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    That's a really good question. I wish I knew the answer!

    I'll keep an eye out for formulations of spinfoam QG that don't use the Immirzi parameter.
     
  11. Apr 25, 2015 #10
    kodama wave function is formulated with y = i.
    with y =i can you get twistor space and twistor theory out of complex gr
     
  12. Apr 25, 2015 #11

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    I suspect that you can and I think that is the direction in which Wolfgang Wieland is working. I can't say definitely because I don't understand his papers well enough. He has been on a postdoc fellowship at Penn State (Ashtekar's group) and will be taking a postdoc position at Perimeter later this year.
    His work seems aimed at a twistorial formulation of spinfoam QG with Hamiltonian.
    I would say he's interested in combining advantages of different approaches into a single formulation. (Ordinary spinfoam QG does not have a Hamiltonian, it is a method to calculate transition amplitudes for processes within boundary conditions specified e.g. by initial and final measurements. Wieland reformulates spinfoam QG so that it has a Hamiltonian similar to canonical LQG. He has also tried using the Ashtekar self-dual formulation. Unfortunately I can't say I understand how this works, so may not be able to respond usefully if you have questions about it!)
     
  13. Apr 25, 2015 #12

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    BTW Kodama, you see the green B I U....Σ bar at the top of the reply box. If you haven't tried it yet, try clicking on the Σ to get a symbol menu. Then you can get things like hbar ħ which is right at the end of the greek letters just before the arrows.
    Also it gives an easy way to use the lower case greek gamma γ and β (both of which are used for the Immirzi parameter in LQG.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Four-Dimensional Entropy from Three-Dimensional Gravity
  1. Dimensional Model (Replies: 1)

Loading...