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

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

2001-03-26

arxiv.org/abs/hep-th/0103209v2

Phys.Rev.D64:086004,2001

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 27 pages, 1 figure

Scientific paper

10.1103/PhysRevD.64.086004

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.

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