Abstract
We consider the physical combinatorics of critical lattice models and their associatedconformal field theories arising in the continuum scaling limit. As examples, we considerA-type unitary minimal models and the level-1 Wess–Zumino–Witten (WZW) model. The Hamiltonian of the WZW model is the invariant XXX quantum spin chain. For simplicity, we consider these theories only in theirvacuum sectors on the strip. Combinatorially, fermionic particles are introduced ascertain features of RSOS paths. They are composites of dual-particles and exhibitthe properties of quasiparticles. The particles and dual-particles are identified,through a conjectured energy-preserving bijection, with patterns of zeros of theeigenvalues of the fused transfer matrices in their analyticity strips. The associated(m,n) systems arise as geometric packing constraints on the particles. The analyticity encodedin the patterns of zeros is the key to the analytic calculation of the excitationenergies through the thermodynamic Bethe ansatz (TBA). As a by-product ofour study, in the case of the WZW or XXX model, we find a relation betweenthe location of the Bethe root strings and the location of the transfer matrix2-strings.
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