A Twisted Affine Interpolation of the ℤ₂²-graded Integrable Super-Liouville and super-Sinh-Gordon Equations

@misc{aizawa2026twisted,
  title = {{A Twisted Affine Interpolation of the $\mathbbZ_2^2$-graded Integrable Super-Liouville and super-Sinh-Gordon Equations}},
  author = {Naruhiko Aizawa and Ren Ito and Luiza Miranda and Francesco Toppan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33485},
  eprint = {2610.33485},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33485},
}

TY  - UNPB
TI  - A Twisted Affine Interpolation of the ℤ_2^2-graded Integrable Super-Liouville and super-Sinh-Gordon Equations
AU  - Naruhiko Aizawa
AU  - Ren Ito
AU  - Luiza Miranda
AU  - Francesco Toppan
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33485
UR  - https://arxiv.org/abs/2610.33485
AB  - This paper is a third one in a series devoted to the construction of 2D, ℤ_2^2-graded, integrable Toda field theories. The first paper introduced parabosonic models obtained from Rittenberg-Wyler color Lie algebras; the second paper explained how to deal with parafermions (the ℤ_2^2-graded super-Liouville theory) from finite Rittenberg-Wyler color Lie superalgebras. This new paper extends the construction to the infinite case of (twisted) affine color Lie superalgebras. A ℤ_2^2-graded extension of osp(2|2)^(2)̂ allows to interpolate the super-Liouville and the super-Sinh-Gordon models, recovered as special limits. The ℤ_2^2-graded extensions of three frameworks are here discussed: the Polyakov's soldering, the Leznov-Savel'ev Lax pair (zero-curvature) formulation and the Bäcklund transformations. As a byproduct of the construction, the Hamiltonian reduction from the ℤ_2^2-graded osp(2|2)^(2)̂ WZNW models induces a ℤ_2^2-graded color Lie superalgebra which admits three inequivalent superVirasoro subalgebras; they are the cal N=2 superVirasoro, the (1,3/2,3/2,2) ℤ_2^2-graded superVirasoro and the (3/2,3/2,2,2) ℤ_2^2-graded superVirasoro.
ER  -