Related papers: Symmetric Spaces of Exceptional Groups
Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory. The 12-dimensional EFT associated to the group $SL(2)\times\mathbb{R}^+$ together with its action is…
In six dimensions, there is an exotic $\mathcal{N}=(4,0)$ supermultiplet that contains only fields of spin $\leq 2$, but no graviton, and that on a circle reduces to 5D $\mathcal{N}=4$ supergravity. It has been proposed that, if suitable…
Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The…
By exploiting suitably constrained Zorn matrices, we present a new construction of the algebra of sextonions (over the algebraically closed field $\mathbb{C}$). This allows for an explicit construction, in terms of Jordan pairs, of the…
We classify $N{=}1$ $d=4$ kinematical and aristotelian Lie superalgebras with spatial isotropy, but not necessarily parity nor time-reversal invariance. Employing a quaternionic formalism which makes rotational covariance manifest and…
We show by explicit construction the existence of various four dimensional models of type II superstrings with N=2 supersymmetry, purely vector multiplet spectrum and no hypermultiplets. Among these, two are of special interest, at the…
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For…
Symmetry group of Lie algebras and superalgebras constructed from (\epsilon,\delta) Freudenthal- Kantor triple systems has been studied. Especially, for a special (\epsilon,\epsilon) Freudenthal- Kantor triple, it is SL(2) group. Also,…
We give a new construction of the Lie algebra of type $E_8$, in terms of $3\times3$ matrices, such that the Lie bracket has a natural description as the matrix commutator. This leads to a new interpretation of the Freudenthal-Tits magic…
Regular polytopes, the generalization of the five Platonic solids in 3 space dimensions, exist in arbitrary dimension $n\geq-1$; now in {\rm dim}. 2, 3 and 4 there are \emph{extra} polytopes, while in general dimensions only the…
The nontrivial unital composition superalgebras, of dimension 3 and 6, which exist only in characteristic 3, are obtained from the split Cayley algebra and its order 3 automorphisms, by means of the process of semisimplification of the…
We present a nonlinear realization of E_8 on a space of 57 dimensions, which is quasiconformal in the sense that it leaves invariant a suitably defined ``light cone'' in 57 dimensions. This realization, which is related to the Freudenthal…
A new structure, based on joining copies of a group by means of a \emph{twist}, has recently been considered to describe the brackets of the two exceptional real Lie algebras of type $G_2$ in a highly symmetric way. In this work we show…
We present the historical path from General relativity to the construction of Maximal $\mathcal{N}_4 = 8$ Supergravity with a detour in D=10 and 11 dimensions. The supergravities obtained by toric dimensional reduction and/or by reducing…
Generalized parallelizable spaces allow a unified treatment of consistent maximally supersymmetric truncations of ten- and eleven-dimensional supergravity in generalized geometry. Known examples are spheres, twisted tori and hyperboloides.…
We classify symmetric backgrounds of eleven-dimensional supergravity up to local isometry. In other words, we classify triples (M,g,F), where (M,g) is an eleven-dimensional lorentzian locally symmetric space and F is an invariant 4-form,…
I will discuss the emergence of lorentzian symmetric spaces as supersymmetric supergravity backgrounds. I will focus on supergravity theories in dimension 11, 10, and 6, and will concentrate on the determination of the so-called maximally…
We exploit the relation among irreducible Riemannian globally symmetric spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions. IRGS appear as scalar manifolds of the theories, as well as moduli spaces of the various…
Recently proposed exceptional field theories (EFTs) making manifest the duality $E_{n(n)}$ symmetry, first observed as nonlinearly realized symmetries of the maximal $d=3,4,...,9$ supergravity ($n=11-d$) and containing 11D and type IIB…
We consider supergravity theories with 16 supercharges in Minkowski space with dimensions $d>3$. We argue that there is an upper bound on the number of massless modes in such theories depending on $d$. In particular we show that the rank of…