Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory

Details Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory

1994-06-03

arxiv.org/abs/hep-th/9406020v1

Phys.Lett. B338 (1994) 448-456

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LaTeX, USC-94/4, PUPT-1469

Scientific paper

10.1016/0370-2693(94)90799-4

We study the description of the $SU(2)$, level $k=1$, Wess-Zumino-Witten conformal field theory in terms of the modes of the spin-1/2 affine primary field $\phi^\alpha$. These are shown to satisfy generalized `canonical commutation relations', which we use to construct a basis of Hilbert space in terms of representations of the Yangian $Y(sl_2)$. Using this description, we explicitly derive so-called `fermionic representations' of the Virasoro characters, which were first conjectured by Kedem et al.~\cite{kedem}. We point out that similar results are expected for a wide class of rational conformal field theories.

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