We generalize the previously studied cosmological solutions in D -dimensional gravity with an antisymmetric (p+2)form to the case when the spatial part of the metric is Ricci-flat rather than flat. These generalized solutions are characterized by a parallel self-dual or anti-self-dual charge density form Q of rank 2m and satisfy the condition Q > 0. As with the previous flat-space case, these e...

LetA be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write A( ) for the space of solutions of the system Au= 0 in a domain X. Using reproducing kernels related to various Hilbert structures on subspaces of A( ), we show explicit identifications of the dual spaces. To prove the regularity of reproducing kernels up to the boundary of , we specify t...

We find explicit AdS4 solutions of massive type IIA with N = 2 supersymmetry obtained deforming with a Roman mass the type IIA supersymmetric reduction of the M theory background AdS4 ×M111. The family of solutions have SU(3) × SU(3) structure and isometry SU(3) × U(1)2. They are conjectured to be dual to three-dimensional N = 2 Chern-Simons theories with generic Chern-Simons couplings and gaug...

We study the String dual to N = 1 SQCD deformed by a quartic superpotential in the quark superfields. We present a unified view of the previous results in the literature and find new exact solutions and new asymptotic solutions. Then we study the Physics encoded in these backgrounds, giving among other things a resolution to an old puzzle related to the beta function and a sufficient criteria f...

This is a review of our previous works [FFR, F1, F3] (some of them joint with B. Feigin and N. Reshetikhin) on the Gaudin model and opers. We define a commutative subalgebra in the tensor power of the universal enveloping algebra of a simple Lie algebra g. This algebra includes the hamiltonians of the Gaudin model, hence we call it the Gaudin algebra. It is constructed as a quotient of the cent...

We consider the self-dual Yang-Mills equations in seven dimensions. Modifying the t’Hooft construction of instantons in d = 4, we find N -instanton 7d solutions which depend on 8N effective parameters and are E6-invariant.

We explain how to construct solutions to the self-dual Einstein vacuum equations from solutions of various two-dimensional integrable systems by exploiting the fact that the Lax formulations of both systems can be embedded in that of the self-dual Yang–Mills equations. We illustrate this by constructing explicit self-dual vacuum metrics on R × Σ, where Σ is a homogeneous space for a real subgro...

In this letter we discuss the supersymmetry issue of the self-dual supermembranes in (8 + 1) and (4 + 1)-dimensions. We find that all genuine solutions of the (8 + 1)-dimensional supermembrane, based on the exceptional group G 2 , preserve one of the sixteen supersymmetries while all solutions in (4 + 1)-dimensions preserve eight of them.

We study the conditions for the fivebrane worldvolume theory in D=11 to admit supersymmetric solitons with non-vanishing self-dual three-form. We construct some new soliton solutions consisting of “superpositions” of calibrated surfaces, self-dual strings and instantons.