# Kähler potential

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

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

It turns out that, for every Káhler manifold, there will exist a coordinate neighborhood  of any given 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 $ds^{2}=dzd{\overline{z}}$.

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.

## References

• 1 T. Barreiro, B. de Carlos & E. J. Copeland, “On non-perturbative corrections to the Kähler potential” Physical Review D57 (1998): 7354 - 7360
Title Kähler potential KahlerPotential 2013-03-22 16:33:17 2013-03-22 16:33:17 rspuzio (6075) rspuzio (6075) 7 rspuzio (6075) Definition msc 53D99 Kahler potential