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

SIGMA 15 (2019), 073, 16 pages      arXiv:1904.09323      https://doi.org/10.3842/SIGMA.2019.073

A Kähler Compatible Moyal Deformation of the First Heavenly Equation

Marco Maceda and Daniel Martínez-Carbajal
Departamento de Física, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco 186, C.P. 03340, Deleg. Iztapalapa, Mexico City, México

Received June 07, 2019, in final form September 08, 2019; Published online September 22, 2019

Abstract
We construct a noncommutative Kähler manifold based on a non-linear perturbations of Moyal integrable deformations of $D=4$ self-dual gravity. The deformed Kähler manifold preserves all the properties of the commutative one, and we obtain the associated noncommutative Kähler potential using the Moyal deformed gravity approach. We apply this construction to the Atiyah-Hitchin metric and its Kähler potential, which is useful in the description of interactions among magnetic monopoles at low energies.

Key words: heavenly equations; Moyal deformation; Atiyah-Hitchin metric.

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