Spectral dualities in XXZ spin chains and five dimensional gauge theories. (English) Zbl 1342.81310
Summary: Motivated by recent progress in the study of supersymmetric gauge theories we propose a very compact formulation of spectral duality between XXZ spin chains. The action of the quantum duality is given by the Fourier transform in the spectral parameter. We investigate the duality in various limits and, in particular, prove it for \(q \to 1\), i.e., when it reduces to the XXX/Gaudin duality. We also show that the universal difference operators are given by the normal ordering of the classical spectral curves.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
Keywords:
lattice integrable models; duality in gauge field theories; supersymmetric gauge theory; quantum groupsReferences:
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