QCD1+1 with massless quarks and gauge covariant Sugawara construction

We use the Hamiltonian framework to study massless QCD1+1, i.e. Yang-Mills gauge theories with massless Dirac fermions on a cylinder (=(1+1) dimensional spacetime S1×R) and make explicit the full, non-perturbative structure of these quantum field theory models. We consider NF fermion flavors and gauge group either U(NC, SU(NC) or another Lie subgroup of U(NC). In this approach, anomalies are traced back to kinematical requirements such as positivity of the Hamiltonian, gauge invariance, and the condition that all observables are represented by well-defined operators on a Hilbert space. We also give equal time commutators of the energy-momentum tensor and find a gauge-covariant form of the (affine-) Sugawara construction. This allows us to represent massless QCD1+1 as a gauge theory of Kac-Moody currents and prove its equivalence to a gauged Wess-Zumino-Witten model with a dynamical Yang-Mills field.