Related papers: The exceptional Jordan algebra and the matrix stri…
A Lagrangian description of a maximally supersymmetric conformal field theory in three dimensions was constructed recently by Bagger and Lambert (BL). The BL theory has SO(4) gauge symmetry and contains scalar and spinor fields that…
Let C be a commutative ring with unity. In this article, we show that every Jordan derivation over an upper triangular matrix algebra T_n(C) is an inner derivation. Further, we extend the result for Jordan derivation on full matrix algebra…
We review known factorization results in quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, the QR factorization. We prove there is a Schur factorization for commuting…
We propose a M(atrix) model for N=4 $SU(k)$ Super-Yang-Mills theory compactified on $T^4$. In this model it is possible to make $T^4$ noncommutative and it is easy to turn on all 6 components of the noncommutativity on $T^4$. The action of…
The matrix model formulation of M-theory can be generalized by compactification to ten-dimensional type II string theory, formulated in the infinite momentum frame. Both the type IIA and IIB string theories can be formulated in this way. In…
An algebra A not encountered in either the usual algebraic varieties or supervarieties is introduced. A is a graded and deformed version of the quaternions, with structure similar to that of a Jordan-Lie superalgebra as defined by Okubo and…
We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, achieved by multiplying one of the gamma matrices by the imaginary number, $i$. The reason for doing this is to…
Let $M_n$ be the algebra of $n \times n$ complex matrices. We consider arbitrary subalgebras $\mathcal{A}$ of $M_n$ which contain the algebra of all upper-triangular matrices (i.e.\ block upper-triangular subalgebras), and their Jordan…
Mirror symmetry was first observed in worldsheet string constructions and shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi-Yau manifolds. It opened…
Based on the realization of three-algebras in terms of algebra of matrices and four-brackets [arXiv:0807.1570] we present the notion of u(N)-based extended three-algebras, which for N=2 reproduces the Bagger-Lambert three-algebra. Using…
We propose and develop a new method to classify orbits of the spin group ${\rm Spin}(2d)$ in the space of its semi-spinors. The idea is to consider spinors as being built as a linear combination of their pure constituents, imposing the…
We study total and partial supersymmetry breaking by freely acting orbifolds, or equivalently by Scherk-Schwarz compactifications, in type I string theory. In particular, we describe a four-dimensional chiral compactification with…
We study exceptional algebroids in the context of warped compactifications of type IIA string theory down to $n$ dimensions, with $n\le 6$. In contrast to the M-theory and type IIB case, the relevant algebroids are no longer exact, and…
The new class of integrable mappings and chains is introduced. Corresponding (1+2) integrable systems invariant with respect to such discrete transformations are represented in explicit form. Soliton like solutions of them are represented…
A rich pattern of gauge symmetries is found in the moduli space of heterotic string toroidal compactifications, at fixed points of the T-duality transformations. We analyze this pattern for generic tori, and scrutinize in full detail…
A new highly symmetrical model of the compact Lie algebra $\mathfrak{g}^c_2$ is provided as a twisted ring group for the group $\mathbb{Z}_2^3$ and the ring $\mathbb{R}\oplus\mathbb{R}$. The model is self-contained and can be used without…
We show that M-theory compactified on a compact Joyce 8-manifold of $Spin(7)$-holonomy, which yields an effective theory in $D = 3$ with $\N$ = 1 supersymmetry, admits at some special points in it moduli space a description in terms of type…
We invoke probe brane arguments to classify the asymptotic behavior of general five-dimensional supergravity theories with eight supercharges near infinite distance boundaries of the vector multiplet moduli space. Imposing consistency of…
The Jordan--Wigner transformation plays an important role in spin models. However, the non-locality of the transformation implies that a periodic chain of $N$ spins is not mapped to a periodic or an anti-periodic chain of lattice fermions.…
We consider a construction of the fundamental spin representations of the simple Lie algebras $\mathfrak{so}(n)$ in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a…