Abstract

The talk will begin with a brief review of Quantum Chromodynamics (QCD) and the Confinement problem. Lattice Gauge Theory (LGT) provides a non-perturbative formulation of QCD , which has led to good numerical results for the low-lying hadron spectra. Yet, an analytical understanding of QCD is not available. The 1+1 dimensional gauge theories have served as useful models of quark confinement. I will revisit the classic Schwinger model and its lattice Hamiltonian formulation. A mass shift between the lattice and continuum definitions of mass, which is motivated by the anomalous chiral symmetry, is shown to lead to improved results. I will also present the zero-temperature phase diagram of the two-flavor Schwinger model at theta=pi, which exhibits dimensional transmutation and spontaneous breaking of charge conjugation. Finally, I will discuss the 2D SU(N) gauge theory coupled to an adjoint multiplet of Majorana fermions. This model has a rich topological structure. I will introduce a Hamiltonian lattice approach to this gauge theory, in which one can compute the spectrum, the string tension, and other observables. The talk will end with some surprising exact results for this model.