Restrictions on Gauge Groups in Noncommutative Gauge Theory
Keizo Matsubara
TL;DR
This paper demonstrates that certain classical gauge groups cannot be implemented in flat noncommutative geometries, highlighting fundamental limitations in noncommutative gauge theories.
Contribution
It establishes the impossibility of realizing SU(N), SO(N), and Sp(N) gauge groups on flat noncommutative manifolds, expanding understanding of gauge group restrictions.
Findings
SU(N), SO(N), Sp(N) cannot be realized on flat noncommutative manifolds
U(N) gauge groups are compatible with noncommutative geometry
The work clarifies fundamental limitations in noncommutative gauge theories
Abstract
We show that the gauge groups SU(N), SO(N) and Sp(N) cannot be realized on a flat noncommutative manifold, while it is possible for U(N).
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