Details
| Original language | English |
|---|---|
| Pages (from-to) | 505-537 |
| Number of pages | 33 |
| Journal | Journal of high energy physics |
| Volume | 7 |
| Issue number | 12 |
| Publication status | Published - 1 Dec 2003 |
Abstract
We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space ℝθ 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 ℝθ 2n×S2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on ℝθ 2n. In the SO(3)-invariant case the vortices on ℝ θ2n determine multi-instantons on ℝθ2n×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 ℝθ2n into spherical D2-branes on ℝθ2n×S2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on ℝθ2n×S2 provide a physical interpretation of the Adams operations in K-theory.
Keywords
- D-branes, Integrable Field Theories, Non-Commutative Geometry, Solitons Monopoles and Instantons
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Journal of high energy physics, Vol. 7, No. 12, 01.12.2003, p. 505-537.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Noncommutative instantons in higher dimensions, vortices and topological K-cycles
AU - Lechtenfeld, Olaf
AU - Popov, Alexander D.
AU - Szabo, Richard J.
N1 - Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2003/12/1
Y1 - 2003/12/1
N2 - We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space ℝθ 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 ℝθ 2n×S2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on ℝθ 2n. In the SO(3)-invariant case the vortices on ℝ θ2n determine multi-instantons on ℝθ2n×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 ℝθ2n into spherical D2-branes on ℝθ2n×S2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on ℝθ2n×S2 provide a physical interpretation of the Adams operations in K-theory.
AB - We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space ℝθ 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 ℝθ 2n×S2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on ℝθ 2n. In the SO(3)-invariant case the vortices on ℝ θ2n determine multi-instantons on ℝθ2n×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 ℝθ2n into spherical D2-branes on ℝθ2n×S2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on ℝθ2n×S2 provide a physical interpretation of the Adams operations in K-theory.
KW - D-branes
KW - Integrable Field Theories
KW - Non-Commutative Geometry
KW - Solitons Monopoles and Instantons
UR - http://www.scopus.com/inward/record.url?scp=23044465746&partnerID=8YFLogxK
U2 - 10.1088/1126-6708/2003/12/022
DO - 10.1088/1126-6708/2003/12/022
M3 - Article
AN - SCOPUS:23044465746
VL - 7
SP - 505
EP - 537
JO - Journal of high energy physics
JF - Journal of high energy physics
SN - 1029-8479
IS - 12
ER -