Asymptotic Safety for Quantum Gravity

[stevendaryl]

Sabine Hossenfelder recently wrote about an old theory of quantum gravity due to Weinberg: asymptotically safe quantum gravity. Is anyone familiar with this idea? What I couldn't figure out from the article is whether asymptotic safety is an approach to making consistent quantum field theories, or whether some quantum field theories just happen to be asymptotically safe. Was Weinberg just hoping/speculating that gravity is asymptotically safe, or was he suggesting a research program to develop an asymptotically safe theory that has the correct low-energy limit?

 

[atyy]

It may just happen to be that some QFTs are asymptotically safe. For example, QCD is believed to be asymptotically free, which is a special sort of asymptotic safety. All indications are that quantum general relativity is not asymptotically free. However, we cannot rigourously rule out that it is not asymptotically safe, with a non-trivial fixed point at high energies. Non-rigorous calculations suggest that (some form of) quantum general relativity is asymptotically safe. (I used "some form of" because there is more than one action that produces classical general relativity.)

An example of a non-trivial fixed point is the Wilson-Fisher fixed point. An example of an asymptotically safe theory is the Gross-Neveu model.

 

[ohwilleke]

Asymptotically safety is something that arises in respect to the renormalization of a constant in a physical theory. If you go to arbitrarily high energies, there are two possibilities - you get infinities (not asymptotically safe), or the values converge towards a finite limit (asymptotically safe).

At a heuristic conceptual level an asymptotic safety feature of a theory is a bit like special relativity which causes everything else to get screwed (time slows down and distances are tweaked) at velocities approaching the speed of light which is the asymptotic limit of the speed of anything in the universe.

The energy scale at which the finite asymptote is reached (for quantum gravity at least and possibly for all of the forces) is assumed to be somewhere in the general vicinity of the GUT scale.

What I couldn't figure out from the article is whether asymptotic safety is an approach to making consistent quantum field theories, or whether some quantum field theories just happen to be asymptotically safe.

Asymptotic safety is a feature of the theory. It is not necessary for a mathematically consistent quantum field theory, but a quantum field theory that is asymptotically safe does have some characteristics that make it attractive (like an absence of singularities where you don't want them to be). A self-aware theoretical physicist is generally going to know with a little bit of investigation if a particular theory is asymptotically safe fairly early on in devising or investigating it. Sometimes it is a feature that the physicist will care a lot about in devising the theory, while other times this may be incidental to other design criteria and just happen to pop up when focusing on other design criteria for a mathematically consistent quantum field theory.

If you are using a "top down" construction of a theory, you would start at the high energy asymptote and work your way down to lower energies. If you are using a "bottom up" construction of a theory, you would generalize your low energy theory to higher energies and start to observe asymptotic behavior emerge as you approach very high energies.