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arXiv:hep-th/9401154 · Physics Letters B

Yangian symmetry in conformal field theory

Kareljan Schoutens

Published Jul 1, 1994• 62 citations
arXivHTMLPDF
DOI
10.1016/0370-2693(94)91061-8

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A bstract In these notes we study integrable structures of conformal field theory with BCD symmetry. We realise these integrable structures as gl \mathfrak{gl} gl gl (1) affine Yangian “spin chains” with boundaries. We provide three solutions of Sklyanin KRKR equation compatible with the affine Yangian R -matrix and derive Bethe ansatz equations for the spectrum. Our analysis provides a unified approach to the integrable structures with BCD symmetry including superalgebras.
The SU(n) quantum chains with inverse-square exchange exhibit a novel form of Yangian symmetry compatible with periodic boundary conditions, allowing states to be countable. We characterize the ``supermultiplets'' of the spectrum in terms of generalized ``occupation numbers.'' We embed the model in the k=1 SU(n) Kac-Moody algebra and obtain a new classification of the states of conformal field theory, adapted to particlelike elementary excitations obeying fractional statistics.