Is the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded sine-Gordon equation integrable?

Abstract

We examine the question of the integrability of the recently defined ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded sine-Gordon model, which is a natural generalisation of the supersymmetric sine-Gordon equation. We do this via appropriate auto-Bäcklund transformations, construction of conserved spinor-valued currents and a pair of infinite sets of conservation laws.

Accepted for publication in Nuclear Physics B. 8 pages, comments still welcomed

References in corpus (3)

• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Once more on parastatistics
• On integrability aspects of the supersymmetric sine-Gordon equation

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• Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics
• $\mathcal{N}=2$ Double graded supersymmetric quantum mechanics via dimensional reduction
• An integrable hierarchy associated with loop extension of ${\mathbb{Z}}_2^2$-graded $\mathfrak{osp}(1|2)$
• Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework