Abstract

BCOVs Feynman rule is a conjectural algorithm used to compute the higher genus Gromov-Witten invariants of Calabi-Yau threefolds. The Feynman graph that appears in BCOVs rule can beinterpreted as a form of geometric quantization. In this presentation, l will attempt to extract it fromthe A-model perspective and realize it as Giventals R-matrix quantization action. Finally. l wilexplain how mixed field theory applies to this quantization formalism of the Feynman rule. This talkis based on a series of joint works with H.-L. Chang, j. Li, W.-P. Li, and Y. Zhou.