Noncommutative gauge theories with Endomorphism algebras

Abstract

We formulate a Yang-Mills action principle for noncommutative connections on an endomorphism algebra of a vector bundle. It is shown that there is an influence of the topology of the vector bundle onto the structure of the vacuums of the theory in a non common way. This model displays a new kind of symmetry breaking mechanism. Some mathematical tools are developed in relation with endomorphism algebras and a new approach of the usual Chern-Weil homomorphism in topology is given.

27 Pages

Cited by in corpus (2)

• D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds
• Dynamics of D-branes I. The non-Abelian Dirac-Born-Infeld action, its first variation, and the equations of motion for D-branes --- with remarks on the non-Abelian Chern-Simons/Wess-Zumino term