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

Olaf Lechtenfeld, Alexander D. Popov, Richard J. Szabo

Research output: Contribution to journalArticle

Abstract

We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space R?2n×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 R?2n×S2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on R?2n. In the SO(3)-invariant case the vortices on R ?2n determine multi-instantons on R?2n×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 R?2n into spherical D2-branes on R?2n×S2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on R?2n×S2 provide a physical interpretation of the Adams operations in K-theory. © SISSA/ISAS 2003.

Original languageEnglish
Pages (from-to)505-537
Number of pages33
JournalJournal of High Energy Physics
Volume7
Issue number12
Publication statusPublished - 1 Dec 2003

Keywords

  • D-branes
  • Integrable Field Theories
  • Non-Commutative Geometry
  • Solitons Monopoles and Instantons

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