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arXiv · hep-th/9108009

Solving 3+1 QCD on the Transverse Lattice Using 1+1 Conformal Field Theory

Paul A. Griffin
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Abstract

A new transverse lattice model of $3+1$ Yang-Mills theory is constructed by introducing Wess-Zumino terms into the 2-D unitary non-linear sigma model action for link fields on a 2-D lattice. The Wess-Zumino terms permit one to solve the basic non-linear sigma model dynamics of each link, for discrete values of the bare QCD coupling constant, by applying the representation theory of non-Abelian current (Kac-Moody) algebras. This construction eliminates the need to approximate the non-linear sigma model dynamics of each link with a linear sigma model theory, as in previous transverse lattice formulations. The non-perturbative behavior of the non-linear sigma model is preserved by this construction. While the new model is in principle solvable by a combination of conformal field theory, discrete light-cone, and lattice gauge theory techniques, it is more realistically suited for study with a Tamm-Dancoff truncation of excited states. In this context, it may serve as a useful framework for the study of non-perturbative phenomena in QCD via analytic techniques.

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Paul A. Griffin. 1991-08-20. Solving 3+1 QCD on the Transverse Lattice Using 1+1 Conformal Field Theory. https://doi.org/10.1016/0550-3213(92)90320-b

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