Particles in RSOS paths

Abstract

We introduce a new representation of the paths of the Forrester-Baxter RSOS models which represents the states of the irreducible modules of the minimal models M(p',p). This representation is obtained by transforming the RSOS paths, for the cases p> 2p'-2, to new paths for which horizontal edges are allowed at certain heights. These new paths are much simpler in that their weight is nothing but the sum of the position of the peaks. This description paves the way for the interpretation of the RSOS paths in terms of fermi-type charged particles out of which the fermionic characters could be obtained constructively. The derivation of the fermionic character for p'=2 and p=kp'+/- 1 is outlined. Finally, the particles of the RSOS paths are put in relation with the kinks and the breathers of the restricted sine-Gordon model.

15 pages, few typos corrected, version published

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• A quartet of fermionic expressions for $M(k,2k\pm 1)$ Virasoro characters via half-lattice paths
• Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization
• Path representation of su(2)_k states I: Operators and particles for k=1,2