Related papers: Non-Abelian Geometry
In this paper we explicitly show the equivalence between the non-Abelian Born-Infeld action, which was proposed by Tseytlin as an effective action on several D-branes, and its noncommutative counterpart for slowly varying fields. This…
We discuss aspects of the algebraic geometry of compact non-commutative Calabi-Yau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi-Yau algebra. We…
We describe the geomety of a set of scalar fields coupled to gravity. We consider the formalism of a differential Z_2-graded algebra of $2\times 2$ matrices whose elements are differential forms on space-time. The connection and the…
In the first part of this article, the geometry of Lie algebroids as well as the Moyal-Weyl star product and some of its generalizations in open string theory are reviewed. A brief introduction to T-duality and non-geometric fluxes is…
We elaborate on the class of deformed T-dual (DTD) models obtained by first adding a topological term to the action of a supercoset sigma model and then performing (non-abelian) T-duality on a subalgebra $\tilde{\mathfrak{g}}$ of the…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
We derive the Seiberg-Witten map to first order in the non-commutativity parameter for D-branes in the presence of a large R-R background field. This result enables a systematic investigation of the commutative formulation of the…
It is known that when there are several D-branes, their space-time coordinates in general become noncommutative. From the point of view of noncommutative geometry, it reflects noncommutativity of the world volume of the D-branes. On the…
A noncommutative algebra $A$, called an algebraic noncommutative geometry, is defined, with a parameter $\epsilon$ in the centre. When $\epsilon$ is set to zero, the commutative algebra $A^0$ of algebraic functions on an algebraic manifold…
We study non-abelian discrete flavor symmetries, which can appear in magnetized brane models. For example, $D_4$, $\Delta(27)$ and $\Delta(54)$ can appear and matter fields with several representations can appear. We also study the orbifold…
In contrast to the world-sheet of a fundamental string, the world-volume of stacked D-branes carries an Azumaya noncommutative structure ([L-Y1: Sec.\ 2] (D(1))), allowing it to directly serve as a probe into noncommutative target-spaces.…
We study all possible deformations of the Maxwell algebra. In D=d+1\neq 3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1,1)\oplus so(d,1) or to so(d,2)\oplus so(d,1) depending on the signs…
A systematic construction is given for N=1 open string boundary coupling to Abelian and non-Abelian Dp-brane worldvolume fields, in general curved backgrounds. The basic ingredient is a set of four ``boundary vectors'' that provide a…
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum…
We define noncommutative gerbes using the language of star products. Quantized twisted Poisson structures are discussed as an explicit realization in the sense of deformation quantization. Our motivation is the noncommutative description of…
We define a noncommutative and nonanticommutative associative product for general supersymplectic forms, allowing the explicit treatment of non(anti)commutative field theories from general nonconstant string backgrounds like a graviphoton…
We study all possible deformations of the Maxwell algebra. In D=d+1\neq 3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1,1)\oplus so(d,1) or to so(d,2)\oplus so(d,1) depending on the signs…
Non-Abelian fractional supersymmetry algebra in two dimensions is introduced utilizing $U_q(sl(2,\Rcc))$ at roots of unity. Its representations and the matrix elements are obtained. The dual of it is constructed and the corepresentations…
In the context of a noncommutative differential calculus on the algebra of real valued functions of an $n$-dimensional manifold $M$, a commutative and associative product of 1-forms is naturally defined. Ordinary differential calculus…
We develop an approach to noncommutative algebraic geometry ``in the perturbative regime" around ordinary commutative geometry. Let R be a noncommutative algebra and A=R/[R,R] its commutativization. We describe what should be the formal…