Integrable Z 2 2 -graded extensions of the Liouville and Sinh–Gordon theories
Naruhiko Aizawa, Ren Ito, Zhanna Kuznetsova, Toshiya Tanaka, Francesco Toppan
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Source: Crossref
Published: Jan 27, 2025
DOI: 10.1088/1751-8121/adaab3
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Abstract In this paper we present a general framework to construct integrable Z 2 2 -graded extensions of classical, two-dimensional Toda and conformal affine Toda theories. The scheme is applied to define the extended Liouville and Sinh–Gordon models; they are based on Z 2 2 -graded color Lie algebras and their fields satisfy a parabosonic statistics. The mathematical tools here introduced are the Z 2 2 -graded covariant extensions of the Lax pair formalism and of the Polyakov’s soldering procedure. The Z 2 2 -graded Sinh–Gordon model is derived from an affine Z 2 2 -graded color Lie algebra, mimicking a procedure originally introduced by Babelon-Bonora to derive the ordinary Sinh–Gordon model. The color Lie algebras under considerations are: the 6-generator Z 2 2 -graded sl 2 , the Z 2 2 -graded affine s l 2 ^ algebra with two central extensions, the Z 2 2 -graded Virasoro algebra obtained from a Hamiltonian reduction.
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