A note on static dyonic diholes

In this brief note we argue that a dyonic generalization of the Emparan-Teo dihole solution is described by a static diagonal metric and therefore, contrary to the claim made in a recent paper by Cabrera-Munguia et al., does not involve any "non-vanishing global angular momentum" and rotating charges.Comment: 4 pages, 1 figure; typos corrected, matches the published versio

Towards Noncommutative Linking Numbers Via the Seiberg-Witten Map

In the present work some geometric and topological implications of noncommutative Wilson loops are explored via the Seiberg-Witten map. In the abelian Chern-Simons theory on a three dimensional manifold, it is shown that the effect of noncommutativity is the appearance of $6^n$ new knots at the $n$-th order of the Seiberg-Witten expansion. These knots are trivial homology cycles which are Poincar\'e dual to the high-order Seiberg-Witten potentials. Moreover the linking number of a standard 1-cycle with the Poincar\'e dual of the gauge field is shown to be written as an expansion of the linking number of this 1-cycle with the Poincar\'e dual of the Seiberg-Witten gauge fields. In the process we explicitly compute the noncommutative 'Jones-Witten' invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the Aharonov-Bohm effect. It is explicitly displayed at first order in the noncommutative parameter, we also show the relation to the noncommutative Landau levels.Comment: 19 pages, 1 figur