Physics NotePublished
Integrable -graded super-Liouville Equation and Induced -graded super-Virasoro Algebra
Naruhiko Aizawa; Ichi Fujii; Ren Ito; Toshiya Tanaka; F. Toppan
Publication details
- Authors
- Naruhiko Aizawa; Ichi Fujii; Ren Ito; Toshiya Tanaka; F. Toppan
- Type
- Physics Note
- Status
- Published
- Publication date
- 23/12/2025
- Description
- 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 $\Z2$-$\osp(1|2).$
- Year
- 2025
- Number
- CBPF-NF-004/25
- Linked to a thesis
- No
- Linked to a grant
- No