TL;DR
This paper investigates the effects of noncommutativity on the moduli-space metric of a charge-two sector in a deformed CP^1 sigma model, revealing the removal of singularities present in the commutative case.
Contribution
It provides an analysis of the noncommutative Kähler potential, including summation of series to obtain analytic expressions, and shows how noncommutativity alters the moduli space structure.
Findings
Noncommutativity removes the logarithmic singularity at the origin.
Analytic expressions for the Kähler potential are obtained in special cases.
The singularity is possibly eliminated entirely for nonzero noncommutativity.
Abstract
We analyze the moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP^1 sigma model in 1+2 dimensions. After carefully reviewing the commutative results of Ward and Ruback, the noncommutative K"ahler 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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