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Longitudinal Rescaling, Integrability and Confinement


In the limit as the number of transverse dimensions goes to zero, Yang-Mills
theory reduces to a 1+1-dimensional model, which is asymptotically free and
completely integrable. Integrability is exploited to study a confining gauge
theory in 2+1 dimensions and a crude model of high-energy scattering in 3+1
dimensions. The latter model arises from QCD by applying a large
longitudinal rescaling. Anomalous dimensions of this rescaling have been
calculated to one loop.