Kähler potential

A Kähler potential is a real-valued function $f$ defined on some coordinate patch of aHermitean manifold such that the metric of the manifold is given by the expression

$$g_{ij*}=\frac{{\partial }^{2}f}{d{z}^{i}d{\overline{z}}^j}.$$

It turns out that, for every Káhler manifold, there will exist a coordinate neighborhood of anygiven point in which the metric can be expresses in terms of a potential this way.

As an elementary example of a Kähler potential, we may consider $f(z,\overline{z})=z\overline{z}$. This potential gives rise to the flat metric $d{s}^2=dzd\overline{z}$.

Kähler potentials have applications in physics. For example, this function $f(x)=\log (x)+g(x)$ relates to the motion of certain subatomic particles called gauginos.