Some fundamental parameters of particle physics can be experimentally extracted only with aid of lattice gauge theory calculations.
The constraints on the $\rho$
and $\eta$ quark transition parameters require both experimental measurements
and accurate
lattice calculations; a non-zero $\eta$ leads to violation of CP symmetry as
observed in Kaon decays and as needed to explain the matter-antimatter asymmetry
of the universe. Any disagreements between the determinations signal a breakdown
of the standard model of particle physics. Nearly all uncertainties will soon be
dominated by lattice QCD uncertainties which will be very significantly reduced
by the work of this project.

K. Anikeev et al., FERMILAB-Pub-01/197
For further information about lattice gauge theory and weak decays, look here
Last seen a few microseconds after the big bang, the quark gluon plasma is the quarry of the RHIC facility, and can be explored from first principles using lattice gauge theory

The QCD phase diagram from ALICE
For further information about lattice gauge theory and the phase structure of QCD, look here
High energy scattering
experiments have measured the distribution of quarks and gluons in the proton.
Ten
teraflops sustained facilities will enable calculation of the moments of the
distributions from first principles.

The quark and gluon distributions in the proton
For further information about lattice gauge theory and hadron structure of QCD, look here