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

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

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

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

Research output: Contribution to journal › Article › peer-review

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 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

Keywords

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

Cite this

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title = "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×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. {\textcopyright} SISSA/ISAS 2003.",

keywords = "D-branes, Integrable Field Theories, Non-Commutative Geometry, Solitons Monopoles and Instantons",

author = "Olaf Lechtenfeld and Popov, {Alexander D.} and Szabo, {Richard J.}",

year = "2003",

month = dec,

day = "1",

language = "English",

volume = "7",

pages = "505--537",

journal = "Journal of High Energy Physics",

issn = "1029-8479",

publisher = "Springer",

number = "12",

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TY - JOUR

T1 - Noncommutative instantons in higher dimensions, vortices and topological K-cycles

AU - Lechtenfeld, Olaf

AU - Popov, Alexander D.

AU - Szabo, Richard J.

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 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.

AB - 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.

KW - D-branes

KW - Integrable Field Theories

KW - Non-Commutative Geometry

KW - Solitons Monopoles and Instantons

M3 - Article

SN - 1029-8479

VL - 7

SP - 505

EP - 537

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 12

ER -

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

Abstract

Keywords

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