Some remarks on unilateral matrix equations

We briefly review the results of our paper hep-th/0009013: we study certain perturbative solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncommutative algebra, and all coefficients are on the left. Recently such equations have appeared in a discussion of generalized Born-Infeld theories. In particular, two equations, their perturbative solutions and the relation between them are studied, applying a unified approach based on the generalized Bezout theorem for matrix polynomials.Comment: latex, 6 pages, 1 figure, talk given at the euroconference "Brane New World and Noncommutative Geometry", Villa Gualino, Torino, Italy, Oct 2-7, 200

Reality in the Differential Calculus on q-euclidean Spaces

The nonlinear reality structure of the derivatives and the differentials for the euclidean q-spaces are found. A real Laplacian is constructed and reality properties of the exterior derivative are given.Comment: 10 page

Fermi-Bose supersymmetry (supergauge symmetry in four dimensions)

The author explains the ideas of Fermi-Bose supersymmetry and presents examples to show how the construction of realistic models may be attempted. (24 refs)

The Seiberg-Witten Map for Noncommutative Gauge Theories

The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of open bosonic string field theory and possible ramifications of this analogy are briefly mentioned.Comment: 12 pages, talk presented at "Continuous Advances in QCD 2002/Arkadyfest", University of Minnesota, Minneapolis, May 17-23, 2002. A few misprints correcte

Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part I: tensor perturbations

We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form \Sigma_{\k}^n \times {\mathbb R}^+, \Sigma_{\k}^n an $n-$manifold of constant curvature \k. Linear perturbations for this class of space-times can be generally classified into tensor, vector and scalar types. The analysis in this paper is restricted to tensor perturbations.Comment: 14 pages, 4 figure

WZW action in odd dimensional gauge theories

It is shown that Wess-Zumino-Witten (WZW) type actions can be constructed in odd dimensional space-times using Wilson line or Wilson loop. WZW action constructed using Wilson line gives anomalous gauge variations and the WZW action constructed using Wilson loop gives anomalous chiral transformation. We show that pure gauge theory including Yang-Mills action, Chern-Simons action and the WZW action can be defined in odd dimensional space-times with even dimensional boundaries. Examples in 3D and 5D are given. We emphasize that this offers a way to generalize gauge theory in odd dimensions. The WZW action constructed using Wilson line can not be considered as action localized on boundary space-times since it can give anomalous gauge transformations on separated boundaries. We try to show that such WZW action can be obtained in the effective theory when making localized chiral fermions decouple.Comment: 19 pages, text shortened, reference added. Version to appear in PR

Braided Hopf Algebras and Differential Calculus

We show that the algebra of the bicovariant differential calculus on a quantum group can be understood as a projection of the cross product between a braided Hopf algebra and the quantum double of the quantum group. The resulting super-Hopf algebra can be reproduced by extending the exterior derivative to tensor products.Comment: 8 page

Nonabelian Gauge Theories on Noncommutative Spaces

In this paper, we describe a method for obtaining the nonabelian Seiberg-Witten map for any gauge group and to any order in theta. The equations defining the Seiberg-Witten map are expressed using a coboundary operator, so that they can be solved by constructing a corresponding homotopy operator. The ambiguities, of both the gauge and covariant type, which arise in this map are manifest in our formalism.Comment: 14 pages, latex, Talk presented at 2001: A Spacetime Odyssey - Michigan Center for Theoretical Physics, some typos correcte