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


It turns out that, for every Káhler manifold, there will exist a coordinate neighborhoodMathworldPlanetmath 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,z¯)=zz¯. This potential gives rise to the flat metric ds2=dzdz¯.

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.


  • 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