Constructs Yangian descendants for the Haldane-Shastry chain via algebraic Bethe ansatz and derives norms and overlaps formulae.
Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
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abstract
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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cond-mat.stat-mech 1years
2026 1verdicts
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Norms, overlaps and Yangian descendants for the Haldane--Shastry spin chain
Constructs Yangian descendants for the Haldane-Shastry chain via algebraic Bethe ansatz and derives norms and overlaps formulae.