# 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

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

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

Kähler potentials have applications in physics. For example, this function $f(x)=\mathrm{log}(x)+g(x)$ 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 |
---|---|

Canonical name | KahlerPotential |

Date of creation | 2013-03-22 16:33:17 |

Last modified on | 2013-03-22 16:33:17 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 7 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 53D99 |

Synonym | Kahler potential |