Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories

TL;DR

This paper extends noncommutative u*(N) gauge algebras to orthogonal and symplectic types, providing explicit representations and connecting them to string theory via D-brane configurations with orientifolds.

Contribution

It introduces new noncommutative o*(N) and usp*(2N) algebras, their explicit matrix representations, and their realization within superstring theory frameworks.

Findings

Explicit matrix representations of o*(N) and usp*(2N) algebras.

Construction of noncommutative gauge theories based on these algebras.

Embedding of these theories in superstring theory with D-branes and orientifolds.

Abstract

The extension of the noncommutative u*(N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u*(N) can consistently be restricted to o*(N) and usp*(N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the formulation for the corresponding noncommutative gauge field theories are obtained. In addition, we present a D-brane configuration with an orientifold which realizes geometrically our algebraic construction, thus embedding the new noncommutative gauge theories in superstring theory in the presence of a constant background magnetic field. Some algebraic generalizations that may have applications in other areas of physics are also discussed.