Related papers: Split-complex representation of the universal hype…
We expand our previous analysis on fivebrane and membrane instanton solutions in the universal hypermultiplet, including near-extremal multi-centered solutions and mixed fivebrane-membrane charged instantons. The results are most…
Making use of non-perturbative U-duality symmetries of type II strings we construct new `superstring' vacua in three dimensions with N=1 supersymmetry. This has an interpretation as compactifying formally from 13 dimensions (S-theory) on…
The hypermultiplet moduli space in Type IIA string theory compactified on a rigid Calabi-Yau threefold X, corresponding to the "universal hypermultiplet", is described at tree-level by the symmetric space SU(2,1)/(SU(2) x U(1)). To…
We study geometric structures arising from Hermitian forms on linear spaces over real algebras beyond the division ones. Our focus is on the dual numbers, the split-complex numbers, and the split-quaternions. The corresponding geometric…
We introduce a new scenario to solve the hierarchy problem based on $\mathcal{N}=2$, five-dimensional supergravity compactified on Calabi-Yau threefold down from $\mathcal{D}=11$ supergravity. When modeling the universe as a 3-brane…
We propose a recipe to construct matrix representations of Nambu--Lie 3-algebras in terms of irreducible representations of underlying Lie algebra. The case of Euclidean four-dimensional 3-algebra is considered in details. We find that…
We construct examples of symplectic half-flat manifolds on compact quotients of solvable Lie groups. We prove that the Calabi-Yau structures are not rigid in the class of symplectic half-flat structures. Moreover, we provide an example of a…
The electromagnetic fields of the hybrid modes of an optical fiber are reformulated using bi-complex mathematics, which leads to simpler expressions relative to those found with the widely used, conventional complex formulation. Generalized…
There has been recently a surge of interest in Grand Unified Theories on orbifolds of higher dimensional spaces. In particular, the higher dimensional doublet-triplet splitting mechanism has been of much interest. I revisit the superstring…
We extend Hitchin's results on "The self-duality equations on a Riemann surface" (Proc. LMS (3), vol. 55, 1987) to orbifold Riemann surfaces. We prove existence results for orbifold solutions of the Yang-Mills-Higgs equations and construct…
New classes of Lie-Hamilton systems are obtained from the six-dimensional fundamental representation of the symplectic Lie algebra $\mathfrak{sp}(6,\mathbb{R})$. The ansatz is based on a recently proposed procedure for constructing…
We propose methods towards a systematic determination of d dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity…
The N=1 superspace generalization of the 3-brane action in 6 dimensions with partially broken N=2 supersymmetry can be constructed using N=1 chiral, complex linear, or real linear superfields. The physical scalars of these multiplets give…
The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness…
Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…
We analyze the superstring propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear sigma-model and the structure of rational curves on the Calabi-Yau manifold. We study in…
A non-Abelian gauge field framework is proposed using the hypercomplex ring formalism. This extension generates non-compact hyperbolic symmetries, which, alongside the compact gauge symmetries, double the internal degrees of freedom. This…
In four-dimensional F-theory compactifications with N=1 supersymmetry the fields describing the dynamics of space-time filling 7-branes are part of the complex structure moduli space of the internal Calabi-Yau fourfold. We explicitly…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
We consider smooth representations of the unit group $G = \mathcal{A}^{\times}$ of a finite-dimensional split basic algebra $\mathcal{A}$ over a non-Archimedean local field. In particular, we prove a version of Gutkin's conjecture, namely,…