Domain wall fermions is an advanced 5-dimensional formulation which permits spin-1/2 particles with accurate chiral symmetry to be described using the techniques of lattice QCD. The physical states in this formulation are bound to the two, four-dimensional faces at either end of a five-dimensional box. As the extent of the fifth dimension grows, these two four-dimensional faces become more separated and the chiral symmetry of the resulting lattice theory of fermions becomes more exact.
In 1996-2002 a number of calculations were carried out in which the valence quarks (those quarks created as explicit constituents of the mesons or nucleons under study) were described using this domain wall formulation. This initial work suggested that this formulation provided a physically sensible description of the quarks with the expected excellent chiral properties and favorable, continuum-like behavior for both on-shell and off-shell quantities.
The first calculations in which both the valence and sea quarks were treated in using the domain wall formulation were carried out by the Columbia group in the late 1990's to study the finite temperature QCD phase transition. While the results of these calculations appeared realistic, the large-lattice spacings needed for finite temperature work combined with the effects of the dynamical fermions lead to very rough and rapidly fluctuating gauge configurations of a sort that in turn lead to large coupling between the physical quarks on the left and right walls. Such couplings gave sizable violations of chiral symmetry, making the accuracy of the domain wall formulation uncertain.
In 2003 the RIKEN-BNL-Columbia (RBC) collaboration began such dynamical simulation anew, this time targeting the weaker coupling, smoother lattice configurations that are needed for simulations at zero termpeatrure. These initial 2-flavor simulations worked out very well, showing both a very physical behavior and small residual chiral symmetry breaking effects.
Beginning in 2005 The RBC and UKQCD collaborations, working together, extended this work to 2+1 flavors using the Iwasaki gauge action, chosen for the small chiral symmetry breaking it produced and the adequate ergodicity of the topological charge evolution. It is these simulation which are still on-going. Begun on a 16^3 x 32 volume, the initial work was extended to a 24^3 x 64 volume. Now, with the capability of the BG/P computer at the ALCF and joined by the LHPC collaboration these calculations are being extended to a second lattice spacing.
The result is a growing set of gauge ensembles enumerated on the adjoining page, at a variety of quark masses and at two lattice spacings, computed with the physically required combination of up, down and strange sea quarks. These lattice ensembles provide a unique resource for physicists in the USQCD and UKQCD collaborations to pursue a broad range of fundamental questions in particle and nuclear physics. A few of the significant physics results that have already been obtained are listed here. The research performed with these gauge ensembles will become even more important as the recently computed finer lattice ensembles are put to wide use.
The results from the second lattice spacing showed that the errors caused by finite lattice spacing were surprisingly small, at or below the 3% level. However, comparison of computed with experimental quantities such as the pseudoscalar decay constants indicated much larger errors associated with the chiral extrapolation to physical light quark masses. As a result, the next objective of the domain wall fermion configuration generation is use even smaller quark masses and the correspondingly larger volumes required to contain the resulting light pions. New ensembles have been started with pion masses of 180 and 250 MeV and linear extent of 4.5 fm. These large volumes are made practical by working at coarser lattice spacing which is in turn made possible by using a new dislocation supressing determanent ratio (DSDR) gauge action.