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Color Kinematics Duality and Asymptotic Safety

  1. Jun 28, 2015 #1
    So, you'll have to forgive me, but I am an engineer, not a physicist, but I take an interest in quantum gravity. My understanding is primarily conceptual, not mathematical. So if my question is dumb, I apologize. Ok, here goes:

    I'm aware of Zwi Bern's conjectured color-kinematics duality where the color factors of the scattering matrix of a Yang Mills theory are replaced with "kinematic factors," by which one obtains an equivalent SUGRA theory. This procedure can be performed to draw an equivalence between Yang Millks and non-SUGRA Einstein gravity (N=0) with an axion and a dilaton, which are regarded as unphysical and are cancelled via ghost fields. A nice slideshow is available here showing the rough outline of the procedure:

    If this procedure holds water, would it not imply that Einstein gravity when quantized is equivalent to a Yang Mills theory, and therefore asymptotically free? That is, it would possess a gaussian fixed point where the cosmological constant and Newton's constant go to zero?

    This reminded me a little of the Asymptotic Safety scenario where there is both a Gaussian and non-Gaussian fixed point along a certain RG trajectory for Quantum Einstein Gravity.
    http://iopscience.iop.org/1367-2630/focus/Focus on Quantum Einstein Gravity
    Look at the Type IIa trajectory in the diagram that passes through the origin.

    So what I'm thinking is that it seems that in both cases (i.e. Color/Kinematics and Asymsafe) there exists a Gaussian Fixed Point. This result is derived using two fundamentally different methods.

    So I guess what I'm asking is- is there correspondence between the two fixed points derived via two different means? Are they truly the "same" fixed point? Is there a deeper connection here? Some fundamental truth about the RG behavior of gravity, or is it just coincidence?
  2. jcsd
  3. Jun 29, 2015 #2
    A gauge theory is said to have color-kinematic duality, if scattering amplitudes can be written in a form like that in Johansson's slide 4 - where there is a fraction with two factors in the numerator, a color factor and a kinematic factor, with the property that the possible color factors and the possible kinematic factors each separately obey the same algebraic relations.

    Then, if you replace the color factor with another copy of the kinematic factor, you get amplitude formulas for a theory containing gravity. But it's not the same theory as the gauge theory. Most "dualities" are about having two or more ways to describe the same thing, but this one is about two different theories having a mathematical similarity.

    So it's not about showing that Einstein gravity is the exact same theory as some Yang-Mills theory. Also, just being a Yang-Mills theory doesn't imply asymptotic freedom. That is just one possible type of RG behavior.

    I am skeptical of the asymptotic safety program. Jacques Distler has blogged several strong criticisms of its methods and claims, and it also seems to be inconsistent with conventional black hole thermodynamics.

    But it does look like the double copy relation pioneered by Bern et al, is relevant to RG behavior. Various supergravity theories are proving to be better behaved than naive analysis indicated, and it's partly because hidden properties of the amplitudes, like color-kinematic duality, cause unanticipated cancellations of divergences.
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