A K\'ahler Compatible Moyal Deformation of the First Heavenly Equation

Autor: Maceda, Marco, Martínez-Carbajal, Daniel
Rok vydání: 2019
Předmět:
Zdroj: SIGMA 15 (2019), 073, 16 pages
Druh dokumentu: Working Paper
DOI: 10.3842/SIGMA.2019.073
Popis: We construct a noncommutative K\"ahler manifold based on a non-linear perturbations of Moyal integrable deformations of $D=4$ self-dual gravity. The deformed K\"ahler manifold preserves all the properties of the commutative one, and we obtain the associated noncommutative K\"ahler potential using the Moyal deformed gravity approach. We apply this construction to the Atiyah-Hitchin metric and its K\"ahler potential, which is useful in the description of interactions among magnetic monopoles at low energies.
Databáze: arXiv