Related papers: Sugawara-type constraints in hyperbolic coset mode…
We continue the study of the one-dimensional E10 coset model (massless spinning particle motion on E10/K(E10) whose dynamics at low levels is known to coincide with the equations of motion of maximal supergravity theories in appropriate…
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…
The hyperbolic Kac-Moody algebra E10 has repeatedly been suggested to play a crucial role in the symmetry structure of M-theory. Recently, following the analysis of the asymptotic behaviour of the supergravity fields near a cosmological…
In this thesis we study algebraic structures in M-theory, in particular the exceptional Lie algebras arising in dimensional reduction of its low energy limit, eleven-dimensional supergravity. We focus on e8 and its infinite-dimensional…
We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms…
A formal ``small tension'' expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10) where K(E10)…
Recently, the concept of a nonlinear sigma-model over a coset space G/H was generalized to the case where the group G is an infinite-dimensional Kac-Moody group, and H its (formal) `maximal compact subgroup'. Here, we study in detail the…
Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and…
We construct solutions of type-II supergravity based on multiple copies and/or mixings of $\lambda$-deformed coset CFTs on $\mathrm{SO}(n+1)_k/\mathrm{SO}(n)_k$, with $n = 2, 3, 4$. The resulting ten-dimensional geometries contain…
The analysis of the extremal structure of the scalar potentials of gauged maximally extended supergravity models in five, four, and three dimensions, and hence the determination of possible vacuum states of these models is a computationally…
We re-examine previously found cosmological solutions to eleven-dimensional supergravity in the light of the E_{10}-approach to M-theory. We focus on the solutions with non zero electric field determined by geometric configurations (n_m,…
We show that (massive) D=10 type IIA supergravity possesses a hidden rigid SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional reduction to one (time-like) dimension. We explicitly construct the associated locally…
We formulate a ten-dimensional version of Kodaira-Spencer gravity on a Calabi-Yau five-fold that reproduces the classical Maurer-Cartan equation governing supersymmetric heterotic moduli. Quantising this theory's quadratic fluctuations, we…
We review the recently discovered connection between the Belinsky-Khalatnikov-Lifshitz-like ``chaotic'' structure of generic cosmological singularities in eleven-dimensional supergravity and the ``last'' hyperbolic Kac-Moody algebra E(10).…
We compare the dynamics of maximal three-dimensional gauged supergravity in appropriate truncations with the equations of motion that follow from a one-dimensional E10/K(E10) coset model at the first few levels. The constant embedding…
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…
We investigate the generalization of loop gravity's twisted geometries to a q-deformed gauge group. In the standard undeformed case, loop gravity is a formulation of general relativity as a diffeomorphism-invariant SU(2) gauge theory. Its…
We examine the proposal of [29] that M-theory may admit a Sugawara-type current algebra formulation based on $E_{11} \otimes_s l_1$. Motivated by the role of generalized coordinates in E-theory, we ask whether current algebra relations of…
We study scalar potentials and the corresponding vacua of N=10 three dimensional gauged supergravity. The theory contains 32 scalar fields parametrizing the exceptional coset space $\frac{E_{6(-14)}}{SO(10)\times U(1)}$. The admissible…
A set of new canonical variables for $d=11$ supergravity is proposed which renders the supersymmetry variations and the supersymmetry constraint polynomial. The construction is based on the $SO(1,2)\times SO(16)$ invariant reformulation of…