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.

arXiv commentWe 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/

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Cited by in corpus (6)

• Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds
• Virtual cycles of stable (quasi)-maps with fields
• A smooth compactification of the space of genus two curves in projective space via logarithmic geometry and Gorenstein curves
• The logarithmic gauged linear sigma model
• Congruences on K-theoretic Gromov--Witten invariants
• Hodge-Gromov-Witten theory