KAC-MOODY SYMMETRIES OF CRITICAL GROUND-STATES

The symmetries of critical ground states of two-dimensional lattice mo dels are investigated. We show how mapping a critical ground state to a model of a rough interface can be used to identify the chiral symmet ry algebra of the conformal field theory that describes its scaling li mit. This is demonstrated in the case of the six-vertex model, the thr ee-coloring model on the honeycomb lattice, and the four-coloring mode l on the square lattice. These models are critical and they are descri bed in the continuum by conformal field theories whose symmetry algebr as are the su(2)(k=1), su(3)(k=1), and the su(4)(k=1) Kac-Moody algebr a, respectively, Our approach is based on the Frenkel-Kac-Segal vertex operator construction of level-one Kac-Moody algebras.