Kac-Moody Symmetries of Critical Ground States

Abstract

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.

arXiv comment42 pages, RevTex, 14 ps figures, Submitted to Nucl. Phys. B. [FS]

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• Exact Results for Hamiltonian Walks from the Solution of the Fully Packed Loop Model on the Honeycomb Lattice

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