Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization
arXiv:1012.4722 · doi:10.1016/j.nuclphysb.2011.01.027
Abstract
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.
28 pages
References in corpus (25)
- Fermionic Sum Representations for Conformal Field Theory Characters
- Fermionic Quasi-Particle Representations for Characters of
- Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M(ν,ν+1). Exact results
- Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
- Fermionic Character Sums and the Corner Transfer Matrix
- Quantum affine symmetry in vertex models
- Spinons in Conformal Field Theory
- Kinks in the Kondo problem
- Order Parameters of the Dilute A Models
- Spinon basis for higher level SU(2) WZW models
- Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models
- Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
- Crystalizing the Spinon Basis
- The perturbations and of the minimal models and the trinomial analogue of Bailey's lemma
- Critical RSOS and Minimal Models I: Paths, Fermionic Algebras and Virasoro Modules
- Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields
- Conjugate Bailey pairs
- Spectral Decomposition of Path Space in Solvable Lattice Model
- A bijection between paths for the M(p,2p+1) minimal model Virasoro characters
- Particles in RSOS paths
- Paths and partitions: combinatorial descriptions of the parafermionic states
- Fermi-gas interpretation of the RSOS path representation of the superconformal unitary minimal models
- Half-lattice paths and Virasoro characters
- Nonlocal operator basis from the path representation of the M(k+1,k+2) and the M(k+1,2k+3) minimal models
- Path representation of su(2)_k states I: Operators and particles for k=1,2