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


SIGMA 6 (2010), 045, 14 pages      arXiv:1001.3416      http://dx.doi.org/10.3842/SIGMA.2010.045
Contribution to the Special Issue “Noncommutative Spaces and Fields”

The Noncommutative Ward Metric

Olaf Lechtenfeld a, b and Marco Maceda c
a) Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
b) Centre for Quantum Engineering and Space-Time Research, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
c) Departamento de Fisica, UAM-Iztapalapa, A.P. 55-534, C.P. 09340, México D.F., México

Received January 31, 2010, in final form May 27, 2010; Published online June 02, 2010

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.

Key words: noncommutative geometry; CP1 sigma model.

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