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Limit cycles in asymptotic safety?

  1. May 20, 2012 #1


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    Litim and Satz have just addressed a question I've long wondered about.

    Limit cycles and quantum gravity
    Daniel Litim, Alejandro Satz
    We study renormalization group equations of quantum gravity in four dimensions. We find an ultraviolet fixed point in accordance with the asymptotic safety conjecture, and infrared fixed points corresponding to general relativity with positive, vanishing or negative cosmological constant. In a minisuperspace approximation, we additionally find a renormalization group limit cycle shielding the ultraviolet from the infrared fixed points. We discuss implications of this pattern for asymptotically safe gravity in the continuum and on the lattice.

    They have an interesting bit of speculation at the end: "Finally we mention that a degenerate limit cycle oers a new scenario for asymptotic safety in that no ne-tuning of UV initial conditions is required. Instead, all trajectories enter an extended semiclassical regime and lead to a tiny positive cosmological constant in the infrared."
    Last edited: May 20, 2012
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  3. May 21, 2012 #2


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    I also wondered about that with a small add on. Cycle limits, on small scale, would be different from point to point, and would be the origin to all particles.
  4. May 21, 2012 #3


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    Alejandro Satz is an interesting guy. He was one of the bunch of young people who took part in the first Zakopane QG school in 2007, and after he got back from Zako he included an account of it in his blog "Reality Conditions".

    He stopped blogging around January 2008. I think he was completing his PhD dissertation at Nottingham (probably with Kirill Krasnov or John Barrett) at about that time, but I don't remember exactly.

    Research-wise it would not be a surprise for Alejandro to come up with something surprising. There were several smart creative young people in that "first class of Zakopane", I think, and he was one.

    So now he is at Maryland where Ted Jacobson is...

    Here's a link to one of our threads that, in turn, links to Satz' blog:
    I see that Rick Kostecki posted on that thread, one of the organizers of the school and the followup workshop the next year:
    Now at Perimeter, or will be starting this Autumn.
    Last edited: May 21, 2012
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