Over the last several years the structure of the QCD vacuum over different length scales and the mechanisms of confinement have been the focus of intense activity among workers in lattice gauge theory. Lattice gauge theory provides the only available framework for the quantitative investigation of such entirely nonperturbative phenomena. Research in this project is in the areas of QCD improved actions; confinement and QCD vacuum physics; deconfinement transition dynamics; and the quark-gluon plasma in heavy ion collisions. A goal of the proposed research is to further develop systematic procedures that connect the short distance (perturbative) to the long distance (non-perturbative) confining regime in the QCD vacuum. It thus contributes towards directly extracting confinement from QCD, a long-standing goal of theoretical particle physics. It also leads to the construction of improved actions on coarser lattices for accurate determination of string tensions and other observables with reduced discretization errors and computational effort. The second area of the project is that of deconfinement dynamics and heavy ion collisions. The recent experimental discoveries at the Relativistic Heavy Ion Collider (RHIC) have generated wide interest. In particular, the mechanism responsible for the apparent very rapid thermalization in the resulting strongly-coupled quarkgluon plasma above deconfinement remains an unresolved question and the focus of intense activity. Simulation methods for non-equilibrium field theory must be developed to properly address such questions. In this project such novel methods are to be investigated by detailed lattice studies that are a natural continuation of simulations on deconfinement dynamics under previous NSF support.
Broader Impacts of this project are that the proposed research in Lattice Gauge Theory involves state-of-the-art methods in Computational Physics that are of wide applicability in the Natural and Biological Sciences and Engineering. As such it provides excellent training in such techniques to graduate students and postdoctoral fellows. For example, graduate students engaged in previously funded projects by this investigator are currently active in engineering and biological research projects. The project can also serve, as it has in the recent past, as a source for mini projects in computation and statistical physics at the upper division undergraduate level. The interplay between experimental discoveries (RHIC) and theoretical/computational physics present in this project has also provided illustrative material for the principal investigator's outreach activities to high school science teachers and students.
Gauge field theories are the building blocks of the Standard Model of particle physics, our present day theory of elementary particle interactions. Gauge theories possess very rich dynamical behavior. Extracting such complex behavior from the underlying theories can be very challenging and, in general, requires the mathematical formulation of gauge theories on a space-time lattice known as Lattice Gauge Theory. In the work completed under this grant this framework was used to investigate various aspects of the dynamics of gauge theories. The behavior of strongly coupled lattice gauge theories under varying quark content is an open problem of great current interest. For small number of quarks a theory like Quantum Chromodynamics, the theory underlying strong nuclear forces, is strongly coupled at long distances and confines quarks. If the number of quark species is increased, however, drastically different, in particular, non-confining behavior can occur. Determining how and at what critical number of quarks this can occur was investigated and estimates of the critical number of quarks species were obtained in a variety of gauge theories. Another important result obtained under this grant, also independently confirmed by recent Monte Carlo simulations, was to show that, contrary to previous conventional wisdom, a lattice gauge theory at infinitely strong coupling can still possess a symmetry known as chiral symmetry, which results in a massless spectrum of particles, provided the number of quarks is large enough. The behavior of gauge theories under variation in temperature is another important aspect of the physics of gauge theories. There is a critical temperature below which quarks are confined and above which they are not. Determining the so-called critical couplings for this deconfinement transition is an important problem in lattice gauge theory. Under this grant a method was developed for relating different critical couplings, thus allowing their determination by essentially one instead of a series of Monte Carlo simulations. For a variety of theoretical and phenomenological reasons the possibility of breaking the space-time symmetries of relativity theory, and thus obtaining alternative theories of quantum gravity, has received considerable attention in recent years. Under this grant conditions under which breaking of such space-time symmetries can occur were investigated in strongly coupled gauge theories with large matter content.
