Related papers: Octonionic Selfduality for SuperMembranes
Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of eleven dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory…
We investigate the possibility of extending the Ashtekar theory to eight dimensions. Our approach relies on two notions: the octonionic structure and the MacDowell-Mansouri formalism generalized to a spacetime of signature 1+7. The key…
We argue that once octonions are formulated as soft Lie algebras, they may be safely used and the non-associativity can be overcame. The necessary points are: (a) Fixing the direction of action by introducing the \delta operator. (b)…
We construct N=8 supersymmetric mechanics with four bosonic end eight fermionic physical degrees of freedom. Starting from the most general N=4 superspace action in harmonic superspace for the ({\bf 4,8,4}) supermultiplet we find conditions…
We give a Hamiltonian formulation of the new model of $\mathcal{N}=8$ supersymmetric mechanics recently proposed by S.~Fedoruk and E.~Ivanov and show that it possesses the dynamical $\mathcal{N}=8$ superconformal symmetry $osp(8|2)$. The…
We consider Brownian motion on symmetric matrices of octonions, and study the law of the spectrum. Due to the fact that the octonion algebra is nonassociative, the dimension of the matrices plays a special role. We provide two specific…
We review some facts about various T-dualities and sigma models on group manifolds, with particular emphasis on supersymmetry. We point out some of the problems in reconciling Poisson-Lie duality with the bi-hermitean geometry of N=2…
Duality relations are explicitly established relating the Hamiltonians and basis classification schemes associated with the number-conserving unitary and number-nonconserving quasispin algebras for the two-level system with pairing…
We study the dualities for sigma models with fermions and bosons. We found that the generalization of the SO(m,m) duality for D=2 sigma models and the Sp(2n) duality for D=4 sigma models is the orthosymplectic duality OSp(m,m|2 n). We study…
By means of a simple model we investigate the possibility that spacetime is a membrane embedded in higher dimensions. We present cosmological solutions of d-dimensional Einstein-Maxwell theory which compactify to two dimensions. These…
Self-dual 2-forms in D=2n dimensions are characterised by an eigenvalue criterion. The equivalence of various definitions of self-duality is proven. We show that the self-dual 2-forms determine a n^2-n+1 dimensional manifold S_{2n} and the…
Let G be a connected, simply connected Poisson-Lie group with quasitriangular Lie bialgebra g. An explicit description of the double D(g) is given, together with the embeddings of g and g^*. This description is then used to provide a…
We construct novel $7d$ supersymmetric gauge theories which include a Chern-Simons-like term on curved spaces. In order to so, we examine the supersymmetry constraints for E7-branes in type IIA$^*$ theory, rather than making use of an…
We perform a systematic study, in eleven dimensional supergravity, of the geometry of wrapped brane configurations admitting $AdS_2$ limits. Membranes wrapping holomorphic curves in Calabi-Yau manifolds are found to exhibit some novel…
We compare the bosonic and maximally supersymmetric membrane models. We find that in Hoppe regulated form the bosonic membrane is well approximated by massive Gaussian quantum matrix models. In contrast the similarly regulated…
Within the superfield approach, we consider the duality between the supersymmetric Maxwell-Chern-Simons and self-dual theories in three spacetime dimensions. Using a gauge embedding method, we construct the dual theory to the self-dual…
We compare the structures and methods in the theory of causal fermion systems with approaches to fundamental physics based on division algebras, in particular the octonions. We find that octonions and, more generally, tensor products of…
In this paper we study the integrability of a family of models with U(1)xSU(N) symmetry. They admit fermionic and bosonic formulations related through bosonization and subsequent T-duality. The fermionic theory is just the CP^(N-1) sigma…
Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we propose and elaborate on a novel duality between bosonic and fermionic theories in four spacetime dimensions. Starting with a Euclidean lattice…
In addition to the double-dimensional reduction procedure that employs world-volume Killing symmetries of $p$-brane supergravity solutions and acts diagonally on a plot of $p$ versus spacetime dimension $D$, there exists a second procedure…