Related papers: A Lax Operator for $d=2$ $N=2$ Supergravity
For general off-shell N=2 supergravity-matter systems in three spacetime dimensions, a formalism is developed to reduce the corresponding actions from superspace to components. The component actions are explicitly computed in the cases of…
We prove that the field equations of supergravity for purely time-dependent backgrounds, which reduce to those of a one--dimensional sigma model, admit a Lax pair representation and are fully integrable. In the case where the effective…
A nonlinear realization of super $W_{\infty}$ algebra is shown to exist through a consistent superLax formulation of super KP hierarchy. The reduction of the superLax operator gives rise to the Lax operators for $N=2$ generalized super KdV…
The Hodge dual operator, recently introduced for supermanifolds, is used to reformulate super Yang-Mills and supergravity in $D=4$. We first recall the definition of the Hodge dual operator for flat and curved supermanifolds. Then we show…
Relying on the geometrical set up of Special K\"ahler Geometry and Quaternionic Geometry, which I discussed at length in my Lectures at the 1995 edition of this Spring School, I present here the recently obtained fully general form of N=2…
We show that the well known $N=1$ NLS equation possesses $N=2$ supersymmetry and thus it is actually the $N=2$ NLS equation. This supersymmetry is hidden in terms of the commonly used $N=1$ superfields but it becomes manifest after passing…
We develop the geometry of four dimensional N=2 superspace where the entire conformal algebra of SU(2,2|2) is realized linearly in the structure group rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries, extending to…
We reduce the dual version of $D=10$, $N=1$ supergravity coupled to $n$ vector fields to four dimensions, and derive the $SL(2,R)\times O(6,6+n)$ transformations which leave the equations of motion invariant. For $n=0$ $SL(2,R)$ is also a…
A new Lax operator is proposed from the viewpoint of constructing the integrable hierarchies related with N=2 super $W_n$ algebra. It is shown that the Poisson algebra associated to the second Hamiltonian structure for the resulted…
The conditions for N=1 supersymmetry in type II supergravity have been previously reformulated in terms of generalized complex geometry. We improve that reformulation so as to completely eliminate the remaining explicit dependence on the…
We discuss the reduction of N=2 supergravity to N=1, by a consistent truncation of the second gravitino multiplet.
A manifestly $N=2$ supersymmetric coset formalism is introduced to describe integrable hierarchies. It is applied to analyze the super-NLS equation. It possesses an $N=2$ symmetry since it can be obtained from a manifest $N=2$ coset algebra…
Working in the geometric approach, we construct the lagrangians of N=1 and N=2 pure supergravity in four dimensions with negative cosmological constant, in the presence of a non trivial boundary of space-time. We find that the supersymmetry…
All the supersymmetric configurations of pure, ungauged, N=4,d=4 supergravity are classified in a formalism that keeps manifest the S and T dualities of the theory. We also find simple equations that need to be satisfied by the…
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…
We modify the four-dimensional N=1 linearized supergravity in a way that components in each superfield are completely identified with fields in the full superconformal formulation. This identification makes it possible to use both…
Dimensional reduction of gravity theories to $D=2$ along commuting Killing isometries is well-known to be classically integrable. The resulting system typically features a coset $\sigma$-model coupled to a dilaton and a scale factor of the…
We review the remarkable interplay between modular symmetries and supergravity, which has led to major advances in both physics and mathematics in recent decades. Our focus will be on four-dimensional models with $\mathcal{N}=1$ and…
We consider the class of four-dimensional N=2 gauged supergravities whose maximally symmetric ground states leave only one of the two supersymmetries intact. For these theories we derive the low-energy effective action below the scale of…
We preesent a new supersymmetric integrable extensions of the a=4,N=2 KdV hierarchy. The root of the supersymmetric Lax operator of the KdV equation is generalized, by including additional fields. This generalized root generate new…