Kac-Moody symmetries of critical ground states

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