Integrable Z22-graded super-Liouville Equation and Induced Z22-graded super-Virasoro Algebra

Nota de FísicaPublicado

Integrable $\mathbb{Z}_2^2$ -graded super-Liouville Equation and Induced $\mathbb{Z}_2^2$ -graded super-Virasoro Algebra

Naruhiko Aizawa; Ichi Fujii; Ren Ito; Toshiya Tanaka; F. Toppan

23/12/2025

Autores: Naruhiko Aizawa; Ichi Fujii; Ren Ito; Toshiya Tanaka; F. Toppan
Tipo: Nota de Física
Status: Publicado
Data de publicação: 23/12/2025
Descrição: We present a framework for enlarging the construction of $\Z2$-graded classical Toda theory from the class of $\Z2$-graded Lie algebras to the class of $\Z2$-graded Lie superalgebras. This scheme is applied to derive a $\Z2$-graded extension of the super-Liouville equation based on a $\Z2$-graded extension of $\osp(1|2).$ The mathematical tools employed in this work are a $\Z2$-graded version of the zero-curvature formalism and of the Polyakov's soldering procedure. It is demonstrated that both methods yield the same $\Z2$-graded super-Liouville equation. An algebraic construction of solutions to the resulting equations is also presented, together with their B\"acklund transformations. Furthermore, three distinct new $\Z2$-graded extensions of the super-Virasoro algebra are obtained via Hamiltonian reduction of the WZNW currents defined for $\Z2$-$\osp(1|2).$
Ano: 2025
Número: CBPF-NF-004/25
Vínculo com tese: Não
Vínculo com bolsa: Não