Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain

Details Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain

2007-03-27

arxiv.org/abs/hep-th/0703240v2

Nucl.Phys.B782:276-295,2007

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, no figures; corrected some typos

Scientific paper

10.1016/j.nuclphysb.2007.05.007

By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation.

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