Lattice Field Theory and Hadronic Physics

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Numerical studies of non-abelian gauge theories coupled to fermions in different representations of the gauge group will form the central focus of all projects in this proposal. Quantum chromodynamics (QCD) belongs to the class of theories we will investigate. The aim is to understand confinement and chiral symmetry breaking, the two features that help understand mass generation and much of the low energy non-perturbative aspects of these theories. We will consider the SU(N) gauge group and consider the limit of a large number of colors (N). We will couple the gauge theory to quarks in the adjoint representation. Using a phenomenon called reduction, we will be able to numerically study the theory on a single site lattice with the number of quark flavors extended to take on any real value. This will enable us to study conformal and near-conformal theories and help us understand mass generation. The de-confinement transition in QCD is currently under intense experimental investigation and we will study the role of baryonic chemical potential in the large-N limit of QCD. Two-dimensional fermion will be used as a probe to study the strong to weak coupling transition in the large N limit of QCD-like theories. We will study the effect of quark masses in multi-favor QCD and, in particular, consider the case of negative quark masses with the aim of identifying a curve in the space of mass parameters where one has massless pions. Quarks carry a color charge and nuclear matter is formed from the binding of colored quarks mediated by gluons. Quantum chromodynamics (QCD) is the theory that describes the interaction of these color charges. Experiments have shown that quarks come in three colors but all nuclear matter is color neutral. Massless quarks and gluons give rise to nuclear matter that has mass. An understanding of this mass generation is of fundamental importance and this project will address various approaches to this problem by focusing on QCD-like theories in the limit of large number of colors. Such theories are closely related to recent developments in string theory and we will be able to make connections between field theory and string theory. The scientific methods involve analytical calculations and numerical computations. A post-doctoral fellow with prior experience in this area during his/her recent graduate work will be mentored by the PI to work on several aspects of the proposal. Computer clusters will be used for numerical computations and the results obtained as part of this proposal will be presented at international conferences in nuclear and particle physics.