Asymptotic safety on the lattice

[atyy]

Interesting posts from Georg von Hippel at http://latticeqcd.blogspot.com/

Monday, July 11, 2011
Lattice 2011, Day One
"Next was a talk by Jack Laiho on Asymptotic Safety and Quantum Gravity. The concept of asymptotic safety as introduced by Weinberg states that a perturbatively non-renormalisable theory may still be well-defined and possesses predictive power if its renormalisation group flow has an ultraviolet fixed point with a finite number of relevant directions. There is some numerical evidence that gravity might be asymptotically safe with only three parameters. In a Euclidean framework, asymptotic safety corresponds to the existence of a critical point. This scenario has been studied in a number of different formulations, including the Euclidean dynamical triangulations of Ambjorn et al. (which have a crumpled phase with infinite Hausdorff dimension and a branched polymer phase with Hausdorff dimension 2, separated by a first-order phase transition, and hence no hope to describe continuum physics) and the Causal Dynamical Triangulations of Ambjorn and Loll (which have a large-scale solution in the form of de Sitter space, and where the spectral dimension runs from 2 at short scales to 4 at large scales). Jack and his student have studied what happens if one adds a measure term to the Regge action, and have found that there are three phases (collapsed, extended, and branched polymer phase) with the possibility of a critical end point in the phase diagram, which could realize the scenario of asymptotic safety. There is also evidence that the spectral dimensions runs from 4 at large scales to 3/2 at short scales, where the dimension 3/2 would reconcile the requirements of holography and the Bekenstein-Hawking entropy."

Wednesday, July 13, 2011
Lattice 2011, Day Two
"The first speaker was Aleksi Kurkela, who spoke about large extra dimensions and the lattice. Extra dimensions are phenomenologically appealing, but since gauge theories in d>4 are non-renormalisable, they are defined only up to a regularisation. Results from the ε-expansion suggest the existence of a non-Gaussian UV fixed point in higher dimensions, but since d=5 is well outside of the expected convergence radius of the expansion, lattice studies are needed to check this; for the isotropic case it does not appear to be true, but for the anisotropic case there is evidence that it is indeed true."

 

[atyy]

marcus has just https://www.physicsforums.com/showpost.php?p=3475973&postcount=1566":

"Although, as we are in a different regime, we cannot make direct contact to the results of [13], our results show that a non-trivial continuum limit is possible in these models and open a small window of hope on non-causal DT models."

"The link to the numerical results of [13] is unclear, and deserves further exploration, either by pushing the simulations to larger κ_D−2 and larger volumes, or by trying to extend the analytical tools to finite κ_D−2."