Related papers: N = 2 Super $W_{\infty}$ Algebra and its Nonlinear…
We provide the geometric actions for most general N=1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N. This provides a supersymmetrization of any generalized dilaton gravity theory or of any…
General relativity and supergravity become integrable systems after dimensional reduction to two spacetime dimensions. This means the equations of motion can be encoded in the flatness condition for a Lax operator. Nicolai and Warner found…
We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the…
A wide class of N=2 reductions of the supersymmetric KP hierarchy in N=1 superspace is described. This class includes a new N=2 supersymmetric generalization of the Toda chain hierarchy. The Lax pair representations of the bosonic and…
A systematic method of constructing manifestly supersymmetric $1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy equations being…
A proposal for constructing a universal nonlinear ${\hat W}_{\infty}$ algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of $D=4$ Self Dual…
We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the $1/r^2…
The N=1 and N=2 super-Schwarzian derivatives were originally introduced by physicists when computing a finite superconformal transformation of the super stress-energy tensor underlying a superconformal field theory. Mathematicians like to…
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional…
In this paper, we introduce a class of super Adler-type operators associated with the Lie superalgebra $\mathfrak{gl}(m|n)$. We show that these operators generate Poisson vertex superalgebras which are isomorphic to the classical…
We present two different Lax operators for a manifestly N=2 supersymmetric extension of "a=-2" Boussinesq hierarchy . The first is the supersymmetric generalization of the Lax operator of the Modified KdV equation. The second is the…
We construct and classify superconformally covariant differential operators defined on N=2 super Riemann surfaces. By contrast to the N=1 theory, these operators give rise to partial rather than ordinary differential equations which leads…
We define and compute explicitly the classical limit of the realizations of $W_n$ appearing as hamiltonian structures of generalized KdV hierarchies. The classical limit is obtained by taking the commutative limit of the ring of…
A systematic construction of super W-algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by…
We prove that the family of non-linear $W$-algebras $SW(3/2,2)$ which are extensions of the $N=1$ superconformal algebra by a primary supercurrent of conformal weight $2$ can be realized as a quantum Hamiltonian reduction of the Lie…
We prove that any classical affine W-algebra W(g,f), where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of Lax type equations. This is based on the theories of…
We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$ subalgebra (resp. $OSp(1|2)$ superalgebra)…
We study the integrability properties of the one-parameter family of $N=2$ super Boussinesq equations obtained earlier by two of us (E.I. \& S.K., Phys. Lett. B 291 (1992) 63) as a hamiltonian flow on the $N=2$ super-$W_3$ algebra. We show…
The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting $\W$-algebra is a…
We investigate extensions of the N=2 super Virasoro algebra by one additional super primary field and its charge conjugate. Using a supersymmetric covariant formalism we construct all N=2 super W-algebras up to spin 5/2 of the additional…