Hello from The Village at Squaw Valley, where I am at the Lattice 2011 conference.
Having arrived late yesterday (actually early today), I still feel rather tired and would like to ask my readers to ascribe any glaring errors or omissions in todays post to that fact.
The welcome was in a different style from the usual speeches -- we were shown a short movie by Massimo Di Pierro that combined elements of "Star Wars" and the "Powers of 10" educational film with images of topological charge densities measured on the lattice. Also unusual was the announcement of a Tesla card raffle sponsored by nVidia.
After that, the first plenary session started with a talk by Eigo Shintani on the determination of αs from lattice QCD. In fact, currently lattice determinations are dominating the world average for αs(MZ2), although there are some discrepancies with other methods. Shintani focussed mainly on the efforts of the JLQCD collaboration, which is based on measuring the light quark vacuum polarisation using dynamical overlap fermions, which then can be compared directly to an operator product expansion performed in the continuum, and αs can be determined by matching to continuum perturbation theory. Other determinations that have been performed have used the Schrödinger functional (ALPHA, PAC-CS), Wilson loops and lattice perturbation theory (HPQCD), and moments of heavy quark current-current correlators (also HPQCD).
The next speaker was Shou-Cheng Zhang from Stanford, who spoke about a topic condensed matter theory that has some interesting connections to lattice QCD, namely topological insulators and superconductors. These are "materials that realise theoretical ideas" in that they cause concepts that are otherwise the realm of theory to appear in an experimentally accessible context. Examples included the appearance of the 3-dimensional Wilson-Dirac operator in the description of a two-dimensional topological insulator, the possibility to have a QED θ-term with θ=π in a topological superconductor, or the appearance of a Dirac monopole as the image charge of a point charge in front of a topological superconductor. These materials also have the possibility to have an enormous technological impact by creating the possibility of having dissipation-free electron flows at room temperature, which could revolutionised electronics and lead to much faster computers.
The last speaker of the session was Mithat Ünsal talking on large-N volume independence and related ideas. Provided that translation invariance and centre symmetry are not spontaneously broken, there is the possibility of reducing QCD in the limit of infinitely many colours to a large-N matrix model. While the Eguchi-Kawai model and its various extensions have failed due to centre symmetry breaking, there appears to be some hope that some other kinds of matrix models could give new insights into gauge theories.
After the coffee break, the second plenary of the day began with Laurence Yaffe speaking about an approach to heavy-ion collisions that begins with simplifying the complicated situation to the much simpler of colliding shockwaves in N=4 super-Yang-Mills theory, which has a dual description as a collision of gravitational waves via the AdS/CFT correspondence. After thus reducing a non-equilibrium problem in a strongly coupled QFT with an initial-value problem in a classical field theory, it turns out that after applying a number of tricks, Einstein's equations for this situation can be converted into a set of nested ODEs that can be solved numerically.
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 possess 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 realise 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.
The last plenary speaker of the day was Paul Rakow, who spoke about flavour-blindness and the pattern of flavour breaking in Nf=3. Since the masses of the light and strange quarks are not identical, the SU(3) flavour symmetry is explicitly broken. Expanding in this breaking around the symmetric theory and exploiting the representation theory of SU(3) allows one to understand the way the physical point is approached in lattice simulations.
In the afternoon there were parallel sessions.
