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Spinons as Composite Fermions

D. C. Cabra, G. L. Rossini, La Plata

Published Jan 1, 1996• 2 citations
OpenAlex

Abstract

We give an explicit holomorphic factorization of SU(N)1 WZW primaries in terms of gauge invariant composite fermions. In the N = 2 case, we show that these composites realize the spinon algebra. Both in this and in the general case, the underlying Yangian symmetry implies that these operators span the whole Fock space. 1

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Spinons as Composite Fermions

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A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model

Paolo Furlan, Ludmil K. Hadjiivanov, Ivan T. Todorov +1 more

The canonical quantization of the WZNW model provides a complete set of exchange relations in the enlarged chiral state spaces that include the Gauss components $M_\\pm$, ${\\bar M}_\\pm$ of the monodromy matrices $M$, $\\bar M$. Regarded as new dynamical variables, the elements of $M$ and $\\bar M$ cannot be identified -- they satisfy different exchange relations. Accordingly, the two dimensional theory expressed in terms of the left and right movers' fields does not automatically respect monodromy invariance. Continuing our recent work on the subject, we show that the definition of the appropriate physical subspace of the $SU(n)$ WZNW model involves an extended quantum group symmetry in a finite dimensional Fock space. In the simplest ($n=2$) case we explicitly construct the subspace of $U_q(sl(2))\\otimes U_q(sl(2))$ invariant vectors. Monodromy invariance is also restored in a weak sense.

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arXiv:0711.1531•Journal of Physics A Mathematical and Theoretical•Dec 12, 2007•6 citations

A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model

Paolo Furlan, Ludmil K. Hadjiivanov, Ivan T. Todorov

The cannonical quantization of the WZNW model provides a complete set of exchange relation in the enlarged chiral state spaces that include the Gauss components M±, [Formula: see text] of the monodromy matrices M, [Formula: see text]. Regarded as new dynamical variables, the elements of M and [Formula: see text] cannot be identified — they satisfy different exchange relations. Accordingly, the two dimensional theory expressed in terms of the left and right movers' fields does not automatically respect monodromy invariance. Continuing our recent work on the subject we show that the definition of the appropriate physical subspace of the SU(n) WZNW model involves an extended quantum group symmetry in a finite dimensional Fock space. In the simplest (n = 2) case we explicitly construct the subspace of Uq(sl(2)) ⊗ Uq(sl(2)) invariant vectors. Monodromy invariance is also restored in a weak sense.

arXiv:hep-th/9610202•International Journal of Modern Physics A•Jan 10, 1997•13 citations
The canonical quantization of the WZNW model provides a complete set of exchange relations in the enlarged chiral state spaces that include the Gauss components $M_\\pm$, ${\\bar M}_\\pm$ of the monodromy matrices MMM, barM\\bar MbarM. Regarded as new dynamical variables, the elements of MMM and barM\\bar MbarM cannot be identified -- they satisfy different exchange relations. Accordingly, the two dimensional theory expressed in terms of the left and right movers' fields does not automatically respect monodromy invariance. Continuing our recent work on the subject, we show that the definition of the appropriate physical subspace of the SU(n)SU(n)SU(n) WZNW model involves an extended quantum group symmetry in a finite dimensional Fock space. In the simplest (n=2n=2n=2) case we explicitly construct the subspace of Uq(sl(2))otimesUq(sl(2))U_q(sl(2))\\otimes U_q(sl(2))Uq​(sl(2))otimesUq​(sl(2)) invariant vectors. Monodromy invariance is also restored in a weak sense.
The cannonical quantization of the WZNW model provides a complete set of exchange relation in the enlarged chiral state spaces that include the Gauss components M±, [Formula: see text] of the monodromy matrices M, [Formula: see text]. Regarded as new dynamical variables, the elements of M and [Formula: see text] cannot be identified — they satisfy different exchange relations. Accordingly, the two dimensional theory expressed in terms of the left and right movers' fields does not automatically respect monodromy invariance. Continuing our recent work on the subject we show that the definition of the appropriate physical subspace of the SU(n) WZNW model involves an extended quantum group symmetry in a finite dimensional Fock space. In the simplest (n = 2) case we explicitly construct the subspace of Uq(sl(2)) ⊗ Uq(sl(2)) invariant vectors. Monodromy invariance is also restored in a weak sense.