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# 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

Synonym:

Kahler potential

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

53D99*no label found*

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