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.

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

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• Integration on minimal ${\mathbb{Z}}_2^2$-superspace and emergence of space
• On classical $Z_2\times Z_2$-graded Lie algebras
• Inequivalent $Z_2^n$-graded brackets, $n$-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics
• Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics
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• Graded colour Lie superalgebras for solving Lévy-Leblond equations
• ${\mathbb{Z}}_2^2$-graded supersymmetry via superfield on minimal ${\mathbb{Z}}_2^2$-superspace
• Beyond the $10$-fold way: $13$ associative $Z_2\times Z_2$-graded superdivision algebras
• $\mathcal{N}=2$ Double graded supersymmetric quantum mechanics via dimensional reduction
• Affine extensions of ${\mathbb{Z}}_2^2$-graded $osp(1|2)$ and Virasoro algebra
• On the detectability of paraparticles beyond bosons and fermions
• Universal weight systems from a minimal ${\mathbb{Z}}_2^2$-graded Lie algebra
• Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
• An integrable hierarchy associated with loop extension of ${\mathbb{Z}}_2^2$-graded $\mathfrak{osp}(1|2)$