Related papers: $E_{11},K_{11}$ and $EE_{11}$
We formulate the bosonic sector of IIB supergravity as a non-linear realisation. We show that this non-linear realisation contains the Borel subalgebras of SL(11) and $E_7$ and argue that it can be enlarged so as to be based on the rank…
We extend the previously given non-linear realisation of E_{11} for the decomposition appropriate to IIB supergravity to include the ten forms that were known to be present in the adjoint representation. We find precise agreement with the…
We formulate all the five dimensional gauged maximal supergravity theories as non-linear realisations of the semi-direct product of E_{11} and a set of generators which transform according to the first fundamental representation l of…
A lot of developments made during the last years show that Kac-Moody algebras play an important role in the algebraic structure of some supergravity theories. These algebras would generate infinite-dimensional symmetry groups. The possible…
We study possible restrictions on the structure of curvature corrections to gravitational theories in the context of their corresponding Kac--Moody algebras, following the initial work on E10 in Class. Quant. Grav. 22 (2005) 2849. We first…
A coset model based on the hyperbolic Kac-Moody algebra E10 has been conjectured to underly eleven-dimensional supergravity and M theory. In this note we study the canonical structure of the bosonic model for finite- and…
We consider a theory in which supersymmetry is partially spontaneously broken and show that the dynamical fields in the same supersymmetric multiplet as the Goldstino are Goldstone bosons whose corresponding generators are central charges…
We construct the non-linear realisation of the semi-direct product of E11 and its vector representation in its decomposition into the subalgebra GL(7)x SL(5) to find a seven dimensional theory. The resulting equations of motion essentially…
We study the relation between the D8-branes wrapped on an orientable compact manifold $W$ in a massive Type IIA supergravity background and the M9-branes wrapped on a compact manifold $Z$ in a massive d=11 supergravity background from the…
The eleven-dimensional gravitational action invariant under local Poincare transformations is given by the dimensional continuation of the Euler class of ten dimensions. Here we show that the supersymmetric extension of this action leads,…
We study the Borcherds superalgebra obtained by adding an odd (fermionic) null root to the set of simple roots of a simple finite-dimensional Lie algebra. We compare it to the Kac-Moody algebra obtained by replacing the odd null root by an…
Synopsis: (i) how superstring theories are unified by M-theory; (ii) how superstring and supermembrane properties follow from the D=10 and D=11 supersymmetry algebras; (iii) how D=10 and D=11 supergravity theories determine the strong…
Quantum M-theory is formulated using the current algebra technique. The current algebra is based on a Kac-Moody algebra rather than usual finite dimensional Lie algebra. Specifically, I study the $E_{11}$ Kac-Moody algebra that was shown…
The formulation of gravity and M-theories as very-extended Kac-Moody invariant theories encompasses, for each very-extended algebra G+++, two distinct actions invariant under the overextended Kac-Moody subalgebra G++. The first carries a…
The conjectured symmetries of M-theory famously involve (1.) brane-extended super-symmetry (the M-algebra) and (2.) exceptional duality-symmetry (the $\mathfrak{e}_{11}$-algebra); but little attention has been given to their inevitable…
We study the Euclidean supersymmetric D=11 M-algebras. We consider two such D=11 superalgebras: the first one is N=(1,1) self-conjugate complex-Hermitean, with 32 complex supercharges and 1024 real bosonic charges, the second is N=(1,0)…
We work out the decomposition of the indefinite Kac Moody algebras ${E_{10}}$ and ${E_{11}}$ w.r.t. their respective subalgebras $A_9$ and $A_{10}$ at low levels. Tables of the irreducible representations with their outer multiplicities are…
We determine the gauge symmetries of all p-forms in maximal three-dimensional gauged supergravity by requiring invariance of the Lagrangian. It is shown that in a particular ungauged limit these symmetries are in precise correspondence to…
We construct a generalised notion of Kac-Moody algebras using smooth maps from the non-compact manifolds ${\cal M}=$SL$(2,\mathbb R)$ and ${\cal M}=$ SL$(2,\mathbb R)/U(1)$ to a finite-dimensional simple Lie group $G$. This construction is…
We present new families of non-supersymmetric solutions of D=11 supergravity with non-relativistic symmetry, based on six-dimensional Kaehler-Einstein manifolds. In constructing these solutions, we make use of a consistent reduction to a…