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International Journal of Modern Physics B

EXCHANGE ALGEBRA AND EXOTIC SUPERSYMMETRY IN THE CHIRAL POTTS MODEL

Denis Bernard, Vincent Pasquier

Published Apr 1, 1990• 17 citations
Publisher

Abstract

We obtain an exchange algebra for the Chiral Potts model, the elements of which are linear in the parameters defining the rapidity curve. This enables us to connect the Chiral Potts model to a Uq(GL(2)) algebra. On the other hand, looking at the model from the S-matrix point of view relates it to a ZZ N generalisation of the supersymmetric algebra.

DOI
10.1142/s0217979290000437

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We obtain an exchange algebra for the Chiral Potts model, the elements of which are linear in the parameters defining the rapidity curve. This enables us to connect the Chiral Potts model to a Uq(GL(2)) algebra. On the other hand, looking at the model from the S-matrix point of view relates it to a ZZ N generalisation of the supersymmetric algebra.
The Nn(n–1)/2-state R-matrix related to U q( sl (n)) algebra at q2N=1 is presented. Its matrix elements are interpreted as Boltzmann weights of an elementary box of some 2D lattice statistical model and given in terms of [Formula: see text] weights of the "minimal" sl (n) chiral Potts model. The corresponding family of transfer matrices depends on n rapidity variables living on high genus algebraic curves, the latter being defined by n moduli. The Yang-Baxter equation is conjectured to hold.