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arXiv · hep-th/0310267

Noncommutative Instantons in Higher Dimensions, Vortices and Topological K-Cycles

Olaf Lechtenfeld·Alexander D. Popov·Richard J. Szabo
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Abstract

We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space R^{2n}_θx S^2 with finite energy and topological charge. By twisting with a Dirac multi-monopole bundle over S^2, we reduce the Donaldson-Uhlenbeck-Yau equations on R^{2n}_θx S^2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on R^{2n}_θ. In the SO(3)-invariant case the vortices on R^{2n}_θdetermine multi-instantons on R^{2n}_θx S^2. We show that these solutions give natural physical realizations of Bott periodicity and vector bundle modification in topological K-homology, and can be interpreted as a blowing-up of D0-branes on R^{2n}_θinto spherical D2-branes on R^{2n}_θx S^2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on R^{2n}_θx S^2 provide a physical interpretation of the Adams operations in K-theory.

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Olaf Lechtenfeld, Alexander D. Popov, Richard J. Szabo. 2003-12-15. Noncommutative Instantons in Higher Dimensions, Vortices and Topological K-Cycles. https://doi.org/10.1088/1126-6708%2F2003%2F12%2F022

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