Noncommutative SO(n) and Sp(n) Gauge Theories

TL;DR

This paper extends noncommutative gauge theories to include orthogonal and symplectic groups by defining suitable subgroups within noncommutative unitary transformations, using an algebra automorphism related to charge conjugation.

Contribution

It introduces a novel method to formulate noncommutative SO(n) and Sp(n) gauge theories through an algebra automorphism, connecting string theory orientifold projections with noncommutative gauge structures.

Findings

Noncommutative SO(n) and Sp(n) gauge theories are constructible.

The construction uses an algebra automorphism generalizing charge conjugation.

String theory low-energy limits relate to orientifold projections with B-fields.

Abstract

We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommutative unitary gauge transformations even though the gauge potentials and gauge transformations are not valued in the orthogonal and symplectic subalgebras of the Lie algebra of antihermitean matrices. Our construction relies on an antiautomorphism of the basic noncommutative algebra of functions which generalizes the charge conjugation operator of ordinary field theory. We show that the corresponding noncommutative picture from low energy string theory is obtained via orientifold projection in the presence of a non-trivial NSNS B-field.