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Spinons in conformal field theory

Denis Bernard, Vincent Pasquier, Didina Serban

Published Apr 8, 1994• 65 citations
OpenAlex

Abstract

We study the su(2) conformal field theory in its spinon description, adapted to the Yangian invariance. By evaluating the action of the Yangian generators on the primary fields, we find a new connection between this conformal field theory and the Calogero-Sutherland model with su(2) spin. We use this connection to describe how the spinons are the quasi-particles spanning the irreducible Yangian multiplet, and also to exhibit operators creating the N-spinon highest weight vectors.

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Spinon bases in supersymmetric CFTs

Thessa Fokkema, Kareljan Schoutens

Abstract We present a novel way to organise the finite size spectra of a class of conformal field theories (CFT) with  = 2 or (nonlinear)  = 4 superconformal symmetry. Generalising the spinon basis of the SU ( n ) 1 WZW theories, we introduce supersymmetric spinons ( ϕ − , ϕ + ) , which form a representation of the supersymmetry algebra. In each case, we show how to construct a multi-spinon basis of the chiral CFT spectra. The multi-spinon states are labelled by a collection { n j } of (discrete) momenta. The state-content for given choice of { n j } is determined through a generalised exclusion principle, similar to Haldane's ‘motif’ rules for the SU ( n ) 1 theories. In the simplest case, which is the  = 2 superconformal theory with central charge c = 1, we develop an algebraic framework similar to the Yangian symmetry of the SU ( 2 ) 1 theory. It includes an operator H 2 , akin to a CFT Haldane–Shastry Hamiltonian, which is diagonalised by multi-spinon states. In all cases studied, we obtain finite partition sums by capping the spinon-momenta to some finite value. For the  = 2 superconformal CFTs, this finitisation precisely leads to the so-called M k supersymmetric lattice models with characteristic order- k exclusion rules on the lattice. Finitising the c = 2 CFT with nonlinear  = 4 superconformal symmetry similarly gives lattice model partition sums for spin-full Fermions with on-site and nearest neighbour exclusion.

arXiv:1512.07234•Journal of Physics A Mathematical and Theoretical•Jun 6, 2016•3 citations
We study the su(2) conformal field theory in its spinon description, adapted to the Yangian invariance. By evaluating the action of the Yangian generators on the primary fields, we find a new connection between this conformal field theory and the Calogero-Sutherland model with su(2) spin. We use this connection to describe how the spinons are the quasi-particles spanning the irreducible Yangian multiplet, and also to exhibit operators creating the N-spinon highest weight vectors.
Affine and Yangian Symmetries in SU(2)1SU(2)_1SU(2)1​ Conformal Field Theory
In these lectures, we study and compare two different formulations of SU(2)SU(2)SU(2), level k=1k=1k=1, Wess-Zumino-Witten conformal field theory. The first, conventional, formulation employs the affine symmetry of the model; in this approach correlation functions are derived from the so-called Knizhnik-Zamolodchikov equations. The second formulation is based on an entirely different algebraic structure, the so-called Yangian Y(sl2)Y(sl_2)Y(sl2​). In this approach, the Hilbert space of the theory is obtained by repeated application of modes of the so-called spinon field, which has SU(2)SU(2)SU(2) spin $j=\thalf$ and obeys fractional (semionic) statistics. We show how this new formulation, which can be generalized to many other rational conformal field theories, can be used to compute correlation functions and to obtain new expressions for the Virasoro and affine characters in the theory. [Lectures given at the 1994 Trieste Summer School on High Energy Physics and Cosmology, Trieste, July 1994.]
Abstract We present a novel way to organise the finite size spectra of a class of conformal field theories (CFT) with  = 2 or (nonlinear)  = 4 superconformal symmetry. Generalising the spinon basis of the SU ( n ) 1 WZW theories, we introduce supersymmetric spinons ( ϕ − , ϕ + ) , which form a representation of the supersymmetry algebra. In each case, we show how to construct a multi-spinon basis of the chiral CFT spectra. The multi-spinon states are labelled by a collection { n j } of (discrete) momenta. The state-content for given choice of { n j } is determined through a generalised exclusion principle, similar to Haldane's ‘motif’ rules for the SU ( n ) 1 theories. In the simplest case, which is the  = 2 superconformal theory with central charge c = 1, we develop an algebraic framework similar to the Yangian symmetry of the SU ( 2 ) 1 theory. It includes an operator H 2 , akin to a CFT Haldane–Shastry Hamiltonian, which is diagonalised by multi-spinon states. In all cases studied, we obtain finite partition sums by capping the spinon-momenta to some finite value. For the  = 2 superconformal CFTs, this finitisation precisely leads to the so-called M k supersymmetric lattice models with characteristic order- k exclusion rules on the lattice. Finitising the c = 2 CFT with nonlinear  = 4 superconformal symmetry similarly gives lattice model partition sums for spin-full Fermions with on-site and nearest neighbour exclusion.