Noncommutative instantons in higher dimensions, vortices and topological K-cycles

, and

Published 22 December 2003 • Published under licence by IOP Publishing Ltd
, , Citation Olaf Lechtenfeld et al JHEP12(2003)022 DOI 10.1088/1126-6708/2003/12/022

Download Article PDF

Article metrics

343 Total downloads

Share this article

Author affiliations

1 Institut für Theoretische Physik, Universität Hannover, Appelstraße 2, 30167 Hannover, Germany

2 Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow Region, Russia

3 Department of Mathematics, Heriot-Watt University, Scott Russell Building, Riccarton, Edinburgh EH14 4AS, U.K.

Dates

  1. Received 3 November 2003
  2. Accepted 12 December 2003
  3. Published

Buy this article in print

1126-6708/2003/12/022

Abstract

We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space Bbb R2nθ × S2 with finite energy and topological charge. By twisting with a Dirac multi-monopole bundle over S2, we reduce the Donaldson-Uhlenbeck-Yau equations on Bbb R2nθ × S2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on Bbb R2nθ. In the SO(3)-invariant case the vortices on Bbb R2nθ determine multi-instantons on Bbb R2nθ × S2. 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 Bbb R2nθ into spherical D2-branes on Bbb R2nθ × S2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on Bbb R2nθ × S2 provide a physical interpretation of the Adams operations in K-theory.

Export citation and abstract BibTeX RIS

Previous article in issue
Next article in issue
Please wait… references are loading.
10.1088/1126-6708/2003/12/022