Related papers: $E_{11}$, Borcherds algebras and maximal supergrav…
In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view…
We study $D \geq 4$-dimensional half-maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half-maximal $\mathrm{Minkowski}_D$ and…
We apply the Lie algebra expansion method to the $\mathcal{N}=1$ super-Poincar\'e algerba in four dimensions. We define a set of p-brane projectors that induce a decomposition of the super-Poincar\'e algebra preparatory for the expansion.…
We study exceptional torsion in the integral cohomology of a family of p-groups associated to p-adic Lie algebras. A spectral sequence E_r^{*,*}[g] is defined for any Lie algebra g which models the Bockstein spectral sequence of the…
Motivated by the long-term goal of finding holographic descriptions for ${\mathcal N}=1$ and ${\mathcal N}=2$ super QCD, we revisit the subject of ''noncritical'' superstring theory. Focusing on string models with 6d super Poincar\'e…
We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this…
In this paper, the low-energy effective dynamics of M-theory, eleven-dimensional supergravity, is taken off-shell in a manifestly supersymmetric formulation. We show that a previously proposed relaxation of the superspace torsion…
The graph G(p) associated with the p-groups of maximal class is a major tool in their classification. We introduce a subgraph of the graph G(p) called its frame. Its construction is based on the Lazard correspondence. We show that every…
We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class $\mathcal{R}$. Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we…
In this paper we study eleven-dimensional supergravity in its most general form. This is done by implementing manifest supersymmetry (and Lorentz invariance) through the use of the geometric (torsion and curvature) superspace Bianchi…
We construct the non-linear realisation of the semi-direct product of E11 and its vector representation in eleven dimensions and find the dynamical equations it predicts at low levels. These equations are completely determined by the…
We perform a careful investigation of which p-form fields can be introduced consistently with the supersymmetry algebra of IIA and/or IIB ten-dimensional supergravity. In particular the ten-forms, also known as "top-forms", require a…
At the two-derivative order, the group manifold reduction of heterotic supergravity on $S^3$ results in a half-maximal 7D gauged supergravity coupled to three vector multiplets, and a further truncation can be taken to remove the vector…
I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of non-linear realisations and Kac-Moody algebras, I explain how to construct the non-linear realisation based on the Kac-Moody algebra E11 and…
Tensor hierarchy algebras constitute a class of non-contragredient Lie superalgebras, whose finite-dimensional members are the "Cartan-type" Lie superalgebras in Kac's classification. They have applications in mathematical physics,…
We investigate the most general N=1 graded extension of the Poincare algebra, and find the corresponding supersymmetry transformations and the associated superspaces. We find that the supersymmetry for which {Q,Q} = P is not special, and in…
We present a new method for constructing $D$-dimensional minimally superintegrable systems based on block coordinate separation of variables. We give two new families of superintegrable systems with $N$ ($N\leq D$) singular terms of the…
We study the superalgebra of the M-theory on a fully supersymmetric pp-wave. We identify the algebra as the special unitary Lie superalgebra, su(2|4;2,0) or su(2|4;2,4), and analyze its root structure. We discuss the typical and atypical…
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 describe generalizations of the manifestly E_{6(6)} covariant formulation of five-dimensional gauged maximal supergravity with regard to the structure of the vector and tensor fields. We indicate how the group-theoretical structures that…