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arXiv · hep-th/9404159

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

E. Langmann·G. W. Semenoff
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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 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.

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E. Langmann, G. W. Semenoff. 1994-10-05. QCD(1+1) with massless quarks and gauge covariant Sugawara construction. https://doi.org/10.1016/0370-2693(94)90310-7

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