Noncommutative Instantons in Higher Dimensions, Vortices and Topological K-Cycles
Abstract
We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space R^{2n}_\theta x 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}_\theta x S^2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on R^{2n}_\theta. In the SO(3)-invariant case the vortices on R^{2n}_\theta determine multi-instantons on R^{2n}_\theta x 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}_\theta into spherical D2-branes on R^{2n}_\theta x S^2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on R^{2n}_\theta x S^2 provide a physical interpretation of the Adams operations in K-theory.
Keywords
Cite
@article{arxiv.hep-th/0310267,
title = {Noncommutative Instantons in Higher Dimensions, Vortices and Topological K-Cycles},
author = {Olaf Lechtenfeld and Alexander D. Popov and Richard J. Szabo},
journal= {arXiv preprint arXiv:hep-th/0310267},
year = {2011}
}
Comments
1+27 pages; v2: references added, final version to appear in JHEP