QCD(1+1) with massless quarks and gauge covariant Sugawara construction

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 $S^1\times \mathbb{R}$) and make explicite 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.

11 pages, ESI 110 Minor changes (including title); version to appear in Phys. Lett. B

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• Bosonization and QCD in Two Dimensions
• Quantum Hadrondynamics in Two Dimensions
• Gauge Theories on a Cylinder
• Gribov ambiguity and non-trivial vacuum structure of gauge theories on a cylinder
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• Quantum fields with classical interactions
• Chiral Schwinger models without gauge anomalies