QUANTUM KAC-MOODY SYMMETRY IN INTEGRABLE FIELD-THEORIES

We show that just as rational conformal theories are characterised by quantum algebras, integrable deformations of such theories are characterised by quantum affine (i.e. Kac-Moody) algebras. More precisely, we study the perturbation series around the conformal theory and observe that each term can be decomposed by an algebraic trick into a sum of products of holomorphic and antiholomorphic "blocks". For the perturbation giving integrability, the SU(q)(2) describing the conformal theory extends to an SU(q)(2) for the "blocks" of the deformed theory. The primary fields phi-1,n (to which we restrict for simplicity) correspond to level-k integrable representations of SU(q)(2), with q = e(i-pi-alpha+2), alpha+2 = 2p/p', k = p' - 2. Of the two independent null vectors in such a representation one is the BRST closure condition of the conformal theory, while the other reflects the finiteness of the primary operator content of the theory.