The noncommutative ward metric

Olaf Lechtenfeld; Marco Maceda

doi:10.3842/SIGMA.2010.045

The noncommutative ward metric

Olaf Lechtenfeld^*, Marco Maceda

^*Corresponding author for this work

UAM-Iztapalapa

Research output: Contribution to journal › Review article › Research › peer review

Abstract

We analyze the moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP¹ sigma model in 1 + 2 dimensions. After carefully reviewing the commutative results of Ward and Ruback, the noncommutative Kähler potential is expanded in powers of dimensionless moduli. In two special cases we sum the perturbative series to analytic expressions. For any nonzero value of the noncommutativity parameter, the logarithmic singularity of the commutative metric is expelled from the origin of the moduli space and possibly altogether.

Original language	English
Article number	045
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	6
DOIs	https://doi.org/10.3842/SIGMA.2010.045
Publication status	Published - 2010

Keywords

CP sigma model
Noncommutative geometry

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2010.045

Cite this

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title = "The noncommutative ward metric",

abstract = "We analyze the moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP1 sigma model in 1 + 2 dimensions. After carefully reviewing the commutative results of Ward and Ruback, the noncommutative K{\"a}hler potential is expanded in powers of dimensionless moduli. In two special cases we sum the perturbative series to analytic expressions. For any nonzero value of the noncommutativity parameter, the logarithmic singularity of the commutative metric is expelled from the origin of the moduli space and possibly altogether.",

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AU - Maceda, Marco

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AB - We analyze the moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP1 sigma model in 1 + 2 dimensions. After carefully reviewing the commutative results of Ward and Ruback, the noncommutative Kähler potential is expanded in powers of dimensionless moduli. In two special cases we sum the perturbative series to analytic expressions. For any nonzero value of the noncommutativity parameter, the logarithmic singularity of the commutative metric is expelled from the origin of the moduli space and possibly altogether.

KW - CP sigma model

KW - Noncommutative geometry

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U2 - 10.3842/SIGMA.2010.045

DO - 10.3842/SIGMA.2010.045

M3 - Review article

AN - SCOPUS:84896062323

SN - 1815-0659

VL - 6

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 045

ER -

The noncommutative ward metric

Abstract

Keywords

ASJC Scopus subject areas

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