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Applying Integrability to Gauge Theories

Lattice Yang-Mills theories in any dimension may be regarded as coupled 1+1-dimensional integrable field theories. These integrable systems decouple at large center-of-mass energies, where the action becomes effectively anisotropic. This effective action is the high-energy center-of-mass limit of the gauge theory. In 2+1 dimensions, the quark-antiquark potential and the mass spectrum can be calculated, using the exact 1+1-dimensional S-matrix and form factors. The methods are quite similar to those applying integrability in statistical and condensed-matter physics. The high-energy anisotropic action at one loop in 3+1 dimensions has been found using a Wilsonian renormalization method. We briefly discuss the isotropic theory in 2+1 dimensions and the connection with soft scattering in 3+1 dimensions.