Longitudinal Rescaling, Integrability and Confinement Peter Orland Baruch College, City University of New York 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.