Path representation of su(2)_k states I: Operators and particles for k=1,2
arXiv:1010.2462 · doi:10.1016/j.nuclphysb.2010.11.019
Abstract
This is the first of two articles devoted to the analysis of the path description of the states in su(2)_k WZW models, a representation well suited for constructive derivations of the fermionic characters. In this first article, the cases k=1,2 are treated in detail, emphasizing a different description in each case (operators vs particles). For k=1, we first prove, as a side result, the equivalence of two known path representations for the finitized su(2)_1 states by displaying an explicit bijection. An immediate offshoot is the gain of a new and simple weighting for the (Kyoto) path representation that generalizes to level k. The bijection also suggests two operator constructions for the su(2)_1 paths, a local and a nonlocal one, both interrelated. These are formal operators that map a path to another path, so that any path can be obtained by successive applications of these operators on a simple reference (ground-state) path. The nonlocal operator description is the starting point for a direct and elementary derivation of the su(2)_1 spinon character. The second part presents an extensive study of the su(2)_2 paths from their particle point of view, where the particles are defined as the path building blocks. The resulting generating functions appear to provide new (at least superficially) fermionic forms of the characters. In particular, a nice relationship between the sum of the j=0,1 characters at k=2 and the two ones at k=1 is unravelled.
arXiv comment42 pages; v2: minor modifications and few references added; version to appear in Nucl. Phys.B
References in corpus (23)
- Diagonalization of the XXZ Hamiltonian by Vertex Operators
- Fermionic Sum Representations for Conformal Field Theory Characters
- Fermionic Quasi-Particle Representations for Characters of
- Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
- Fermionic Character Sums and the Corner Transfer Matrix
- Spinons in Conformal Field Theory
- Spinon basis for higher level SU(2) WZW models
- Crystalizing the Spinon Basis
- The Many Faces of a Character
- A quasi-particle description of the M(3,p) models
- The Extended Algebra of the SU(2) Wess-Zumino-Witten Models
- Conjugate Bailey pairs
- The Extended Algebra of the Minimal Models
- Spectral Decomposition of Path Space in Solvable Lattice Model
- A monomial basis for the Virasoro minimal series M(p,p') : the case 1<p'/p<2
- Embedding of bases: from the M(2,2k+1) to the M(3,4k+2-delta) models
- Particles in RSOS paths
- Paths and partitions: combinatorial descriptions of the parafermionic states
- A bijection between paths for the M(p,2p+1) minimal model Virasoro characters
- Physical Combinatorics and Quasiparticles
- Fermi-gas interpretation of the RSOS path representation of the superconformal unitary minimal models
- 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 II: Operator construction of the fermionic character and spin-1/2--RSOS factorization