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Twins separated at birth

  1. Oct 7, 2009 #1


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    "Historically speaking, string theory and the loop representation of quantum gravity are twins separated at birth. (Baez, Class. Quantum Grav. 15 (1998) 1827–1858)" :smile:

    Now with AdS/CFT for strings, and group field theory for loops, both can reach their true destiny for describing condensed matter :tongue2:
  2. jcsd
  3. Oct 7, 2009 #2


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    I was kidding, but apparently there is some analogy!

    "The advantage of this formulation of quantum gravity is that it precisely fixes the sum over spin foams, and that it allows a number of theoretical tools from standard quantum field theory to be imported directly into the background independent formalism. In this sense, this approach has similarities with the philosophy of the Maldacena duality in string theory: a nonperturbative theory is dual to a more quantum field theory. But here there is no conjecture involved: the duality between certain spin-foam models and certain group field theories is a theorem. (Rovelli, http://relativity.livingreviews.org/Articles/lrr-2008-5/ [Broken])"
    Last edited by a moderator: May 4, 2017
  4. Oct 7, 2009 #3


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    Dearly Missed

    Last edited by a moderator: May 4, 2017
  5. Oct 7, 2009 #4


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    The proof is supposed to be here:
    Spacetime as a Feynman diagram: the connection formulation
    Michael P. Reisenberger, Carlo Rovelli

    Group field is to spin foam as Boulatov-Ooguri is to Pozano-Regge:
    Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
    R. De Pietri, L. Freidel, K. Krasnov, C. Rovelli

    OK, it's not my policy to cite Rovelli so much since I detest background independence :grumpy: :wink:, so let me cite some other interesting group field theory stuff to balance it out:

    3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
    Winston Fairbairn, Etera R. Livine

    Group field theory renormalization - the 3d case: power counting of divergences
    Laurent Freidel, Razvan Gurau, Daniele Oriti

    Scaling behaviour of three-dimensional group field theory
    Jacques Magnen, Karim Noui, Vincent Rivasseau, Matteo Smerlak

    And to get back to twins separated at birth, let's compare:

    Oriti http://arxiv.org/abs/gr-qc/0607032 "Group field theories were developed at first as a generalisation of matrix models for 2d quantum gravity to 3 and 4 spacetime dimensions to produce a lattice formulation of topological theories. More recently, they have been developed further in the context of spin foam models for quantum gravity"

    McGreevy http://arxiv.org/abs/0909.0518 "Now we can see some similarities between this expansion and perturbative string expansions .......... This story is very general in the sense that all matrix models define something like a theory of two-dimensional fluctuating surfaces via these random triangulations."
    Last edited: Oct 8, 2009
  6. Oct 9, 2009 #5


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    A short review which gives examples of non-commutative geometry in spin foams (section 2.3), condensed matter (2.5), and string theory (2.6):

    Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
    Richard J. Szabo
  7. Oct 9, 2009 #6


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    The cubic matrix model and a duality between strings and loops

    Lee Smolin
    (Submitted on 19 Jun 2000)
    We find evidence for a duality between the standard matrix formulations of M theory and a background independent theory which extends loop quantum gravity by replacing SU(2) with a supersymmetric and quantum group extension of SU(16). This is deduced from the recently proposed cubic matrix model for M theory which has been argued to have compactifications which reduce to the IKKT and dWHN-BFSS matrix models. Here we find new compactifications of this theory whose Hilbert spaces consist of SU(16) conformal blocks on compact two-surfaces. These compactifications break the SU(N) symmetry of the standard M theory compactifications, while preserving SU(16), while the BFSS model preserve the SU(N) but break SU(16) to the SO(9) symmetry of the 11 dimensional light cone coordinates. These results suggest that the supersymmetric and quantum deformed SU(16) extension of loop quantum gravity provides a dual, background independent description of the degrees of freedom and dynamics of the M theory matrix models.


    This paper was never published in a peer review magazine, but it has got 33 citations, mostly from string theorists.
    Last edited: Oct 9, 2009
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