Moduli-space dynamics of noncommutative abelian sigma-model solitons

Michael Klawunn; Olaf Lechtenfeld; Stefan Petersen

doi:10.1088/1126-6708/2006/06/028

Moduli-space dynamics of noncommutative abelian sigma-model solitons

Michael Klawunn^*
, Olaf Lechtenfeld
, Stefan Petersen

^*Corresponding author for this work

Institute of Theoretical Physics

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

Abstract

In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space ^k/S_k features a natural Kähler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.

Original language	English
Article number	028
Journal	Journal of high energy physics
Volume	2006
Issue number	6
DOIs	https://doi.org/10.1088/1126-6708/2006/06/028
Publication status	Published - 1 Jul 2006

Keywords

Integrable Field Theories
Non-Commutative Geometry
Solitons Monopoles and Instantons

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1088/1126-6708/2006/06/028

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abstract = "In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space k/Sk features a natural K{\"a}hler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.",

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N2 - In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space k/Sk features a natural Kähler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.

AB - In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space k/Sk features a natural Kähler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.

KW - Integrable Field Theories

KW - Non-Commutative Geometry

KW - Solitons Monopoles and Instantons

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JF - Journal of high energy physics

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ER -

Moduli-space dynamics of noncommutative abelian sigma-model solitons

Abstract

Keywords

ASJC Scopus subject areas

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