Related papers: Twisted Self-Duality of Dimensionally Reduced Grav…
Geroch's solution-generating method is extended to the case of Einstein spaces, which possess a Killing vector {{}and are thus asymptotically (locally) (anti-)de Sitter}. This includes the reduction to a three-dimensional coset space, the…
The 1--loop string background equations with axion and dilaton fields are shown to be integrable in four dimensions in the presence of two commuting Killing symmetries and $\delta c = 0$. Then, in analogy with reduced gravity, there is an…
Kinnersley--type representation is constructed for the four--dimensional Einstein--Maxwell--dilaton--axion system restricted to space--times possessing two non--null commuting Killing symmetries. New representation essentially uses the…
We study the dimensional reduction of general relativity to a single null spacetime dimension. The dimensionally reduced theory is a theory of six scalar fields governed by three constraints. It has an infinite dimensional symmetry which is…
We review how Geroch's reduction method is extended from Ricci-flat to Einstein spacetimes. The Ehlers-Geroch SL(2,R) group is still present in the three-dimensional sigma-model that captures the dynamics, but only a subgroup of it is…
It is shown how to generate three-dimensional Einstein-Maxwell fields from known ones in the presence of a hypersurface-orthogonal non-null Killing vector field. The continuous symmetry group is isomorphic to the Heisenberg group including…
Starting with the 2+1 Einstein--Maxwell--Dilaton system with a cosmological constant and assuming two commuting Killing symmetries we derive the corresponding $1+0 \sigma$--model. It is shown that, for general values of the coupling…
We apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the vacuum equations as ratios of determinants.…
Einstein-Rosen waves with two polarizations are cylindrically symmetric solutions to vacuum Einstein equations. Einstein equations in this case reduce to an integrable system. In 1971, Geroch has shown that this system admits an…
The algebra A(D-3)+++ dimensionally reduces to the E(D-1) symmetry algebra of (12-D)-dimensional supergravity. An infinite set of five-dimensional gravitational objects trivially embedded in D-dimensions is constructed by identifying the…
Under the action of the Geroch group, the Minkowski metric can be transformed into any vacuum metric with two commuting Killing vectors. In principle, this reduces the problem of deriving vacuum metrics with two commuting Killing vectors to…
Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields…
We examine the properties and symmetries of the lowest order effective theory of 4-dim string backgrounds with axion and dilaton fields and zero cosmological constant. The dimensional reduction yields an O(2,2) current group of…
For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Pleba\'nski based on the Darboux theorem. In the…
We establish a twisted analog of our recent work on vertex representations and the McKay correspondence. For each finite group $\Gamma$ and a virtual character of $\Gamma$ we construct twisted vertex operators on the Fock space spanned by…
It has long been appreciated that the toroidal reduction of any gravity or supergravity to two dimensions gives rise to a scalar coset theory exhibiting an infinite-dimensional global symmetry. This symmetry is an extension of the…
Static axisymmetric Einstein-Maxwell-Dilaton and stationary axisymmetric Einstein-Maxwell-Dilaton-Axion (EMDA) theories in four space-time dimensions are shown to be integrable by means of the inverse scattering transform method. The proof…
We study the Geroch group in the framework of the Ashtekar formulation. In the case of the one-Killing-vector reduction, it turns out that the third column of the Ashtekar connection is essentially the gradient of the Ernst potential, which…
Kac--Moody groups $G$ over $\mathbb{R}$ have been conjectured to occur as symmetry groups of supergravity theories dimensionally reduced to dimensions less than 3, and their integral forms $G(\mathbb{Z})$ conjecturally encode quantized…
All the causally regular geometries obtained from (2+1)-anti-de Sitter space by identifications by isometries of the form $P \rightarrow (\exp \pi\xi) P$, where $\xi$ is a self-dual Killing vector of $so(2,2)$, are explicitely constructed.…