Lattice 2010, Day Four

Today's first plenary session was started by Kazuyuki Kanaya with a talk on finite-temperature QCD. Many groups are looking for the transition temperature between the confined and deconfined phases, but since in the neighbourhood of the physical point, the transition is most likely a crossover, the value of the "critical" temperature found may be dependent on the observable studied. There was further some disagreement even between different studies using the same observables, but those discrepancies seem to have gone mostly away.

Next was Luigi Del Debbio speaking about the conformal window on the lattice. The motivation for those kinds of studies is the hope that the physics of electroweak symmetry breaking by originate not from a fundamental scalar Higgs, but from a fermionic condensate similar to the chiral condensate in QCD arising from a gauge theory ("technicolor") living at higher energy scales, perhaps around 1 TeV. One is then motivated to look for gauge theories having an infrared fixed point. Lattice simulations can help studying the question which combinations of N_c, the number of colours, and N_f, the number of fermion flavours, actually exhibit such behaviour. The Schrödinger functional can be used to study such questions, but while there are a number of results, no very clear picture appears to have emerged yet.

The second plenary session of the morning was opened with a talk on finite-density QCD by Sourendu Gupta. QCD at finite density, i.e. finite chemical potential, is plagued by a sign problem because the fermionic determinant can no longer be real in general. A number of ways around this problem have been proposed. The most straightforward is reweighting, the most ambitious a reformulation of the theory that manages to eliminate the sign problem entirely. On the latter front, there has been progress in that the 3D XY model, which also has a sign problem, has been successfully reformulated in different variables in which it does no longer suffer from its sign problem; whether something similar might be possible for QCD remains to be seen. Other approaches try to exploit analyticity to evade the sign problem, either by Taylor-expanding around zero chemical potential and measuring the Taylor coefficients as susceptibilities at zero chemical potential, or by simulating at purely imaginary chemical potential (where there is no sign problem) and extrapolating to real chemical potential. In this way, various determinations of the critical point of QCD have been performed, which agree more or less with each other. All of them lie in a region through which the freeze-out curve of heavy-ion experiments is expected to pass, so the question of the location of the critical point may become accessible experimentally.

The last plenary talk of the morning was Takeshi Yamazaki talking on a determination of the binding energy of helium nuclei in quenched QCD. The effort involved is considerable (there are more than 1000 different contractions for ⁴He, and the lattices considered have to be very large to be able to accommodate a helium nucleus and to distinguish between true bound states and attractive scattering states), even though the simulations were quenched and the valence quarks used corresponded to a pion mass of about 800 MeV. The study found that helium nuclei are indeed bound.

In the afternoon there were parallel sessions.