Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions

We present the maximally supersymmetric three-dimensional gauged supergravities. Owing to the special properties of three dimensions -- especially the on-shell duality between vector and scalar fields, and the purely topological character of (super)gravity -- they exhibit an even richer structure than the gauged supergravities in higher dimensions. The allowed gauge groups are subgroups of the global E_8 symmetry of ungauged N=16 supergravity. They include the regular series SO(p,8-p) x SO(p,8-p) for all p=0,1,...,4, the group E_8 itself, as well as various noncompact forms of the exceptional groups E_7, E_6 and F_4 x G_2. We show that all these theories admit maximally supersymmetric ground states, and determine their background isometries, which are superextensions of the anti-de Sitter group SO(2,2). The very existence of these theories is argued to point to a new supergravity beyond the standard D=11 supergravity.Comment: 41 pages, LaTeX2e, minor changes, references adde

E8(8)_{8(8)} Exceptional Field Theory: Geometry, Fermions and Supersymmetry

We present the supersymmetric extension of the recently constructed E$_{8(8)}$ exceptional field theory -- the manifestly U-duality covariant formulation of the untruncated ten- and eleven-dimensional supergravities. This theory is formulated on a (3+248) dimensional spacetime (modulo section constraint) in which the extended coordinates transform in the adjoint representation of E$_{8(8)}$. All bosonic fields are E$_{8(8)}$ tensors and transform under internal generalized diffeomorphisms. The fermions are tensors under the generalized Lorentz group SO(1,2)$\times$SO(16), where SO(16) is the maximal compact subgroup of E$_{8(8)}$. Vanishing generalized torsion determines the corresponding spin connections to the extent they are required to formulate the field equations and supersymmetry transformation laws. We determine the supersymmetry transformations for all bosonic and fermionic fields such that they consistently close into generalized diffeomorphisms. In particular, the covariantly constrained gauge vectors of E$_{8(8)}$ exceptional field theory combine with the standard supergravity fields into a single supermultiplet. We give the complete extended Lagrangian and show its invariance under supersymmetry. Upon solution of the section constraint the theory reduces to full D=11 or type IIB supergravity.Comment: 25 page

Integrable structures in classical off-shell 10D supersymmetric Yang-Mills theory

The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness conditions were proposed, which are explicitly integrable (hep-th/9811108), and are based on the breaking of symmetry SO(9,1) -> SO(2,1)xSO(7). In this article, we investigate their physical content. To this end, group-algebraic methods are developed which allow to derive the set of physical fields and their equations of motion from the superfield expansion of the supercurl, systematically. A set of integrable superspace constraints is identified which drastically reduces the field content of the unconstrained superfield but leaves the spectrum including the original Yang-Mills vector field completely off-shell. A weaker set of constraints gives rise to additional fields obeying first order differential equations. Geometrically, the SO(7) covariant superspace constraints descend from a truncation of Witten's original linear system to particular one-parameter families of light-like rays.Comment: 43 pages, 4 figures. Improved version for publicatio

On the Yangian Y(e_8) quantum symmetry of maximal supergravity in two dimensions

We present the algebraic framework for the quantization of the classical bosonic charge algebra of maximally extended (N=16) supergravity in two dimensions, thereby taking the first steps towards an exact quantization of this model. At the core of our construction is the Yangian algebra $Y(e_8)$ whose RTT presentation we discuss in detail. The full symmetry algebra is a centrally extended twisted version of the Yangian double $DY(e_8)_c$. We show that there exists only one special value of the central charge for which the quantum algebra admits an ideal by which the algebra can be divided so as to consistently reproduce the classical coset structure $E_{8(8)}/SO(16)$ in the limit $\hbar\to 0$.Comment: 21 pages, LaTeX2