Related papers: Towards an Ashtekar formalism in eight dimensions
We lay out an infinity categorical interpretation of reconstruction theorems which are germane to the symmetric monoidal perspective of noncommutative algebraic geometry, present sufficient conditions which allow for the factorization of…
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in…
A topological theory for euclidean gravity in eight dimensions is built by enforcing octonionic self-duality conditions on the spin connection. The eight-dimensional manifold must be of a special type, with G_2 or Spin(7) holonomy. The…
In condensed matter theory many invaluable models rely on the possibility of subsuming fundamental particle interactions in constitutive relations for macroscopic fields in near equilibrium assemblies of particles. Should one wish to…
Using (partial) curvature flows and the transitive action of subgroups of O(d,Z) on the indices {1,...,d} of the components of the Yang-Mills curvature in an orthonormal basis, we obtain a nested system of equations in successively higher…
The connection of (split-)division algebras with Clifford algebras and supersymmetry is investigated. At first we introduce the class of superalgebras constructed from any given (split-)division algebra. We further specify which real…
We examine how to construct explicit heterotic string models dual to F-theory in eight dimensions. In doing so we learn about where the moduli spaces of the two theories overlap, and how non-perturbative features leave traces on a purely…
We describe off-shell $\mathcal{N}=1$ M-theory compactifications down to four dimensions in terms of eight-dimensional manifolds equipped with a topological $Spin(7)$-structure. Motivated by the exceptionally generalized geometry…
The Landauer-Butikker formalism is an important formalism to study mesoscopic systems. Its validity for linear transport is well established theoretically as well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)] had…
In this paper I shall consider various possible scalar-vector-tensor field theories which might be used to describe the Universe. After imposing numerous constraints of a physical and mathematical nature on the theories under consideration,…
We construct octonionic multi-instantons for the eight and seven dimensional Yang-Mills theory. Extended soliton solutions to the low-energy heterotic field theory equations of motion are constructed from these octonionic multi-instantons.…
Through timelike dualities, one can generate exotic versions of $M$-theory with different spacetime signatures. These are the $M^*$-theory with signature $(9,2,-)$, the $M'$-theory, with signature $(6,5,+)$ and the theories with reversed…
In this thesis we study embedding formalisms for $\mathcal{N}$-extended anti-de Sitter (AdS) superspaces in four and five dimensions. Specifically, building on earlier work in the four-dimensional case, we develop bi-supertwistor…
A tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.
At the macrosopic level we study candidate 3D effective field theories associated to M theory in three dimensions. These represent analogs of 11D supergravity for eleven dimensional M-theory. At the microscopic level we study various world…
We extend an operator formalism, developed by Hongler, Kyt\"ol\"a, and Zahabi in 2012 for the Ising model, to the Ashkin-Teller and loop $\mathrm{O} ( n ) $ models. The formalism is primarily dependent upon notions of massive, and massless,…
M-theory has different global supersymmetry structures in its various dual incarnations, as characterized by the M-algebra in 11D, the type IIA, type-IIB, heterotic, type-I extended supersymmetries in 10D, and non-Abelian supersymmetries in…
We construct a six-dimensional Maxwell theory using a latticized extra space, the continuum limit of which is a shifted torus recently discussed by Dienes. This toy model exhibits the correspondence between continuum theory and discrete…
The article is devoted to application of tensorial formalism for derivation of different types of Maxwell's equations. The Maxwell's equations are written in the covariant coordinate-free and the covariant coordinate forms. Also the…