E. Langmann, G. W. Semenoff
QCD$_{1+1}$ with Massless Quarks and Gauge Covariant Sugawara Construction
The paper is published: Phys. Letters B 341 (1994) 195-204

MSC:

81T13 Yang-Mills and other gauge theories, See also {53C07,

Abstract: We use the Hamiltonian framework to study massless QCD$_{1+1}$, i.e.\
Yang-Mills gauge theories with massless Dirac fermions on a cylinder
(= (1+1) dimensional spacetime $S^1\times \R$) and make explicit the
full, non-perturbative structure of these quantum field theory
models. We consider $N_F$ fermion flavors and gauge group either
$\U(N_C)$, $\SU(N_C)$ or another Lie subgroup of $\U(N_C)$. 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
QCD$_{1+1}$ 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.

Keywords: quantum chromodynamics, Yang-Mills theory, gauge theory