# Path integral for quantum Mabuchi K-energy

@article{Lacoin2018PathIF,
title={Path integral for quantum Mabuchi K-energy},
author={Hubert Lacoin and R{\'e}mi Rhodes and Vincent Vargas},
journal={Duke Mathematical Journal},
year={2018}
}
• Published 4 July 2018
• Physics, Mathematics
• Duke Mathematical Journal
We construct a path integral based on the coupling of the Liouville action and the Mabuchi K-energy on a one-dimensional complex manifold. To the best of our knowledge this is the first rigorous construction of such an object and this is done by means of probabilistic tools. Both functionals play an important role respectively in Riemannian geometry (in the case of surfaces) and K\"ahler geometry. As an output, we obtain a path integral whose Weyl anomaly displays the standard Liouville anomaly…
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