Hello from the Atahotel Tanka Village Resort in Villasimius, Sardinia, Italy, where I am at the Lattice 2010 conference.
The conference started this morning with a talk by Martin Lüscher about "Topology, the Wilson flow and the HMC algorithm". It is by now well known in the lattice community that Monte Carlo simulations of lattice QCD suffer from a severy problem with long autocorrelations of the topological charge of the gauge field. This problem affects the HMC algorithm and its variants that are used in lattice simulations with dynamical fermions just as well as the simple link updating schemes (Metropolis, heat bath) that can be used for pure gauge or quenched calculations. The autocorrelation time of the topological charge grows roughly like the fifth power of the inverse lattice spacing a as a is taken to zero. This is a real problem because it indicates the presence in the system being simulated of modes that are updates only very slowly, and as a consequence the statistical errors of observables measured from Monte Carlo simulations may be seriously underestimated, because the contribution to the error coming from the long tails of the autocorrelation function that stem from those modes are not properly taken into account. Martin Lüscher then introduced the Wilson flow, which is an evolution in field space generated by the Wilson plaquette action, and which can in some sense be seen as consisting of a sequence of infinitesimal stout link smearings. For the case of an abelian gauge theory, the flow equation can be solved exactly via the heat kernel, and it can be shown that it gives renormalised smooth solutions. For QCD, the same can be seen to be true numerically. Defining a transformed field V(U) by running with the Wilson flow for a specified time t0, it can then be shown that the path integral over U is the same as the path integral over V(U) with an additional term in the action that comes from the Jacobian of the transformation and is proportional to g0/a times the integral of the Wilson plaquette action along the flow trajectory. As a goes to zero, the latter term will act to suppress large value of the plaquette. An old theorem of Lüscher shows that the submanifold of field space with a plaquette values less than 0.067 divides into topological sectors, and hence the probability to be "between" topological sectors decays in line with the suppression of large plaquettes by the g0/a term. This explains the problem seen, but also offers hope for a solution, since one might now try to develop algorithms that make progress by making large changes to the smooth fields V.
This was followed by two review talks. The first was a review of the state of the art in hadron spectroscopy and light pseudoscalar decay constants by Christian Hölbling emphasizing the reduction of systematic errors achieved by decreasing lattice spacings and pion masses and increasing simulation volumes.
The second review talk of the morning was given by Constantia Alexandrou, who reviewed hadron structure and form factor calculations from the lattice, drawing attention to the many remaining uncertainties in this important area, where in particular the axial charge gA of the nucleon is consistently measured to be significantly lower on the lattice than in nature.
The last plenary speaker of the day was Gregorio Herdoiza, who spoke about the progress being made towards 2+1+1 flavour simulations. The collaborations currently pursuing the ambitious goal of including a fully dynamic charm quark in their simulations are ETMC and MILC. MILC is using the Highly Improved Staggered Quark (HISQ) action to reduce discretisation errors, whereas ETMC is relying on a variant of twisted mass fermions with an explicit breaking of the mass degeneracy for the strange/charm doublet. In the former case, the effects of reduced lattice artifacts are clearly seen, while in the latter case the O(a2) mass splitting between the neutral and charged pion increases with the number of flavours. In either case, a significant effort is necessary to tune the strange and charm quark masses to their physical values, but the effort is definitely well-spent if it leads to Nf=2+1+1 predictions from lattice QCD that include all effects of an active charm quark.
In the afternoon there were parallel talks. Two that I'd like to highlight were the talk of Bastian Knipschild from Mainz, who presented an efficient method to strongly reduce the systematic error on nucleon form factors coming from excited state contributions, and David Adam's talk in which he presented a generalisation of the overlap operator to staggered fermions that gives a chiral two-flavour theory.