A K\"ahler Compatible Moyal Deformation of the First Heavenly Equation
Mathematical Physics
2019-09-24 v3 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
We construct a noncommutative K\"ahler manifold based on a non-linear perturbations of Moyal integrable deformations of 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.
Keywords
Cite
@article{arxiv.1904.09323,
title = {A K\"ahler Compatible Moyal Deformation of the First Heavenly Equation},
author = {Marco Maceda and Daniel Martínez-Carbajal},
journal= {arXiv preprint arXiv:1904.09323},
year = {2019}
}