U(1)-supersymmetric extension of the Liouville equation
The paper presents a new integrable system with extended supersymmetry: \(N=2\) supersymmetric extension of the Liouville equation. It is formulated in a covariant fashion in terms of a complex \(N=2\) superfield subjected to the Grassmann analyticity conditions. The zero-curvature representation (on the superalgebra osp(2,2)) together with an associated linear problem are constructed for this system, its general solution is found and the reduction to the previously known \(N=1\) super-Liouville equation is discussed. All the consideration proceeds within a general method based on nonlinear realizations of infinite dimensional symmetries. The \(N=1\) and \(N=2\) super-Liouville equations are shown to support a nonlinear realization of \(N=1\) and \(N=2\) superextensions of the conformal group in two dimensions (associated with the contact superalgebras \({\mathbb{K}}(1,1)\) and \({\mathbb{K}}(1,2)\) from Kac's classification).
scientific article; zbMATH DE number 3859641