Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization

Details 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 II: Operator construction of the fermionic character and spin-1/2--RSOS factorization

2010-12-21

arxiv.org/abs/1012.4722v1

Nucl.Phys.B847:247-273,2011

Physics

High Energy Physics

High Energy Physics - Theory

28 pages

Scientific paper

10.1016/j.nuclphysb.2011.01.027

This is the second of two articles (independent of each other) devoted to the analysis of the path description of the states in su(2)_k WZW models. Here we present a constructive derivation of the fermionic character at level k based on these paths. The starting point is the expression of a path in terms of a sequence of nonlocal (formal) operators acting on the vacuum ground-state path. Within this framework, the key step is the construction of the level-k operator sequences out of those at level-1 by the action of a new type of operators. These actions of operators on operators turn out to have a path interpretation: these paths are precisely the finitized RSOS paths related to the unitary minimal models M(k+1,k+2). We thus unravel -- at the level of the path representation of the states --, a direct factorization into a k=1 spinon part times a RSOS factor. It is also pointed out that since there are two fermionic forms describing these finite RSOS paths, the resulting fermionic su(2)_k characters arise in two versions. Finally, the relation between the present construction and the Nagoya spectral decomposition of the path space is sketched.

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