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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 073, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.073 (Mi sigma1509) 		 
This article is cited in 1 scientific paper (total in 1 paper)

A Kähler Compatible Moyal Deformation of the First Heavenly Equation

Marco Maceda, Daniel Martínez-Carbajal

Departamento de Física, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco 186, C.P. 03340, Deleg. Iztapalapa, Mexico City, México
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DOI: https://doi.org/10.3842/SIGMA.2019.073
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.
Keywords: heavenly equations, Moyal deformation, Atiyah–Hitchin metric.
Funding agency Grant number
Universidad Autónoma Metropolitana
D. Martínez-Carbajal acknowledges support from Universidad Autónoma Metropolitana (UAM, México).
Received: June 7, 2019; in final form September 8, 2019; Published online September 22, 2019
Bibliographic databases:
Document Type: Article
MSC: 37K10, 53C26, 53D55, 70H06, 83C20
Language: English
Citation: Marco Maceda, Daniel Martínez-Carbajal, “A Kähler Compatible Moyal Deformation of the First Heavenly Equation”, SIGMA, 15 (2019), 073, 16 pp.
Citation in format AMSBIB
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\by Marco~Maceda, Daniel~Mart{\'\i}nez-Carbajal
\paper A K\"ahler Compatible Moyal Deformation of the First Heavenly Equation
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\papernumber 073
\totalpages 16
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