Noncommutative multi-instantons on ℝ2n x S2

Tatiana A. Ivanova; Olaf Lechtenfeld

doi:10.1016/S0370-2693(03)00868-2

Noncommutative multi-instantons on ℝ²ⁿ x S²

Tatiana A. Ivanova^*, Olaf Lechtenfeld

^*Corresponding author for this work

Institute of Theoretical Physics

Joint Institute for Nuclear Research

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

Abstract

Generalizing self-duality on ℝ² x S² to higher dimensions, we consider the Donaldson-Uhlenbeck-Yau equations on ℝ ²ⁿ x S² and their noncommutative deformation for the gauge group U(2). Imposing SO(3) invariance (up to gauge transformations) reduces these equations to vortex-type equations for an Abelian gauge field and a complex scalar on ℝ_θ²ⁿ. For a special S ²-radius R depending on the noncommutativity θ we find explicit solutions in terms of shift operators. These vortex-like configurations on ℝ_θ²ⁿ determine SO(3)-invariant multi-instantons on ℝ_θ²ⁿ x S_R² for R = R(θ). The latter may be interpreted as sub-branes of codimension 2n inside a coincident pair of noncommutative Dp-branes with an S² factor of suitable size.

Original language	English
Pages (from-to)	107-115
Number of pages	9
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	567
Issue number	1-2
DOIs	https://doi.org/10.1016/S0370-2693(03)00868-2 https://doi.org/10.1016/S0370-2693(03)00868-2
Publication status	Published - 7 Aug 2003

ASJC Scopus subject areas

Nuclear and High Energy Physics

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Cite this

@article{c805a8552007444fbba6b3f5347790ae,

title = "Noncommutative multi-instantons on ℝ2n x S2",

abstract = "Generalizing self-duality on ℝ2 x S2 to higher dimensions, we consider the Donaldson-Uhlenbeck-Yau equations on ℝ 2n x S2 and their noncommutative deformation for the gauge group U(2). Imposing SO(3) invariance (up to gauge transformations) reduces these equations to vortex-type equations for an Abelian gauge field and a complex scalar on ℝθ2n. For a special S 2-radius R depending on the noncommutativity θ we find explicit solutions in terms of shift operators. These vortex-like configurations on ℝθ2n determine SO(3)-invariant multi-instantons on ℝθ2n x SR2 for R = R(θ). The latter may be interpreted as sub-branes of codimension 2n inside a coincident pair of noncommutative Dp-branes with an S2 factor of suitable size.",

author = "Ivanova, {Tatiana A.} and Olaf Lechtenfeld",

note = "Funding Information: The authors are grateful to A.D. Popov for fruitful discussions and for reading the manuscript. O.L. wishes to thank B.-H. Lee for discussions. T.A.I. acknowledges the Heisenberg-Landau Program for partial support and the Institut f{\"u}r Theoretische Physik der Universit{\"a}t Hannover for its hospitality. This work was partially supported by grant LE-838/7 within the framework of the DFG priority program (SPP 1096) in string theory. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",

year = "2003",

month = aug,

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doi = "10.1016/S0370-2693(03)00868-2",

language = "English",

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pages = "107--115",

journal = "Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics",

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AU - Ivanova, Tatiana A.

AU - Lechtenfeld, Olaf

N1 - Funding Information: The authors are grateful to A.D. Popov for fruitful discussions and for reading the manuscript. O.L. wishes to thank B.-H. Lee for discussions. T.A.I. acknowledges the Heisenberg-Landau Program for partial support and the Institut für Theoretische Physik der Universität Hannover for its hospitality. This work was partially supported by grant LE-838/7 within the framework of the DFG priority program (SPP 1096) in string theory. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2003/8/7

Y1 - 2003/8/7

N2 - Generalizing self-duality on ℝ2 x S2 to higher dimensions, we consider the Donaldson-Uhlenbeck-Yau equations on ℝ 2n x S2 and their noncommutative deformation for the gauge group U(2). Imposing SO(3) invariance (up to gauge transformations) reduces these equations to vortex-type equations for an Abelian gauge field and a complex scalar on ℝθ2n. For a special S 2-radius R depending on the noncommutativity θ we find explicit solutions in terms of shift operators. These vortex-like configurations on ℝθ2n determine SO(3)-invariant multi-instantons on ℝθ2n x SR2 for R = R(θ). The latter may be interpreted as sub-branes of codimension 2n inside a coincident pair of noncommutative Dp-branes with an S2 factor of suitable size.

AB - Generalizing self-duality on ℝ2 x S2 to higher dimensions, we consider the Donaldson-Uhlenbeck-Yau equations on ℝ 2n x S2 and their noncommutative deformation for the gauge group U(2). Imposing SO(3) invariance (up to gauge transformations) reduces these equations to vortex-type equations for an Abelian gauge field and a complex scalar on ℝθ2n. For a special S 2-radius R depending on the noncommutativity θ we find explicit solutions in terms of shift operators. These vortex-like configurations on ℝθ2n determine SO(3)-invariant multi-instantons on ℝθ2n x SR2 for R = R(θ). The latter may be interpreted as sub-branes of codimension 2n inside a coincident pair of noncommutative Dp-branes with an S2 factor of suitable size.

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