Kac-Moody Symmetries of Critical Ground States

Details Kac-Moody Symmetries of Critical Ground States Kac-Moody Symmetries of Critical Ground States

1995-11-21

arxiv.org/abs/cond-mat/9511102v1

Nucl.Phys. B464 (1996) 540-575

Physics

Condensed Matter

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

Scientific paper

10.1016/0550-3213(96)00064-8

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.

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