SUSY FIELD-THEORIES IN HIGHER DIMENSIONS AND INTEGRABLE SPIN CHAINS

Five-and six-dimensional SUSY gauge theories, with one or two compacti fied directions, are discussed. The 5d theories with the matter hyperm ultiplets in the fundamental representation are associated with the tw isted XXZ spin chain, while the group product case with bi-fundamental matter corresponds to the higher rank spin chains. The Riemann surfac es for 6d theories with fundamental matter and two compact directions are proposed to correspond to the XYZ spin chain based on the Sklyanin algebra. We also discuss the obtained results within the brane and ge ometrical engineering frameworks and explain the relation to the toric diagrams. (C) 1998 Elsevier Science B.V.