BCOV's Feynman rule of quintic $3$-folds

Abstract

We prove the BCOV Feynman rule by identifying the Feynman graph sum to the graph sum of an R-matrix action extracted from the NMSP theory. As direct consequences, (i) we obtain the genus one and genus two potentials, and (ii) we prove the two Yamaguchi-Yau equations.

We add to the original version (i) a full argument obtaining the genus two potential, (ii) a short proof that BCOV Feynman rules imply Yamaguchi-Yau equations, and (iii) explicit formulae for R-matrices in appendix. All supplementary material, and additional information related to the NMSP theory, are available at https://sites.google.com/site/guoshuaimath/