Related papers: Algebraic Dreams
We summarise the results of our recent paper (arXiv:1511.08737) highlighting what might be considered to be a Lie-algebraic derivation of eleven-dimensional supergravity.
We solve an open problem in spectral geometry: the construction of finite-dimensional, discrete geometries coordinatized by non-simple, exceptional Jordan algebras. The approach taken is readily generalisable to broad classes of…
Recently, motivated by certain loop quantum gravity inspired corrections, it was shown that for spherically symmetric midisuperspace models infinitely many second derivative theories of gravity exist (as revealed by the presence of three…
We continue the study undertaken in \cite{DV} of the exceptional Jordan algebra $J = J_3^8$ as (part of) the finite-dimensional quantum algebra in an almost classical space-time approach to particle physics. Along with reviewing known…
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…
Starting from the four normed division algebras - the real numbers, complex numbers, quaternions and octonions - a systematic procedure gives a 3-cocycle on the Poincare Lie superalgebra in dimensions 3, 4, 6 and 10. A related procedure…
We analyze maximal supersymmetry in eleven-dimensional supergravity from the point of view of the oriented matroid theory. The mathematical key tools in our discussion are the Englert solution and the chirotope concept. We argue that…
Spacetime superalgebras with 64 or less number of real supercharges, containing the type IIB Poincare superalgebra in (9,1) dimensions and the N=1 Poincare superalgebra in (10,1) are considered. The restriction D<14, and two distinct…
The generalised-geometric formulation of 10-dimensional supergravity suggests a particular simple "limit", which results in a theory whose only dynamical degrees of freedom are the dilaton and the dilatino. The theory is still invariant…
The main obstacle in attempts to construct a consistent quantum gravity is the absence of independent flat time. This can in principle be cured by going out to higher dimensions. The modern paradigm assumes that the fundamental theory of…
We study six-dimensional N=(1,0) supergravity theories with abelian, as well as non-abelian, gauge group factors. We show that for theories with fewer than nine tensor multiplets, the number of possible combinations of gauge groups -…
A global superalgebra with 32 supercharges and all possible central extensions is studied in order to extract some general properties of duality and hidden dimensions in a theory that treats $p$-branes democratically. The maximal number of…
We construct the scalar potential for the exceptional field theory based on the affine symmetry group E$_9$. The fields appearing in this potential live formally on an infinite-dimensional extended spacetime and transform under E$_9$…
We give a formulation of linearized 11D supergravity in 4D, $N=1$ superspace keeping all eleven bosonic coordinates. The fields are fluctuations around $\mathbf M=\mathbf R^{4|4}\times Y$, where $Y$ is a background Riemannian 7-manifold…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
We construct a new extension of the Poincar\'e superalgebra in eleven dimensions which contains super one-, two- and five-form charges. The latter two are associated with the supermembrane and the superfivebrane of M-theory. Using the…
We consider a conformal system of a string and a particle defined in D=10+2 space-time dimensions. The extra time-like dimension is a gauge artifact and can be eliminated by choosing a gauge in which the SO(10,1) Lorentz symmetry is…
Quantum gravity in AdS$_7 \times$S$^4$ is dual to a 6d superconformal field theory, known as the 6d $(2,0)$ theory, which is very challenging to describe because it lacks a conventional Lagrangian description. On the other hand, certain…
A conjectured finite M-theory based on eleven-dimensional supergravity formulated in a superspace with a non-anticommutative <>-product of field operators is proposed. Supermembranes are incorporated in the superspace <>-product formalism.…
Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a…