Polyakov relation for the sphere and higher genus surfaces
High Energy Physics - Theory
2016-09-14 v3 Mathematical Physics
math.MP
Abstract
The Polyakov relation, which in the sphere topology gives the changes of the Liouville action under the variation of the position of the sources, in the case of higher genus is related also to the dependence of the action on the moduli of the surface. We write and prove such a relation for genus 1 and for all hyperelliptic surfaces.
Cite
@article{arxiv.1507.04853,
title = {Polyakov relation for the sphere and higher genus surfaces},
author = {Pietro Menotti},
journal= {arXiv preprint arXiv:1507.04853},
year = {2016}
}
Comments
31 pages;typos corrected;eq.(141) corrected