Quantization of open-closed BCOV theory, I

Understand

This is the first in a series of papers which analyze the problem of quantizing the theory coupling Kodaira-Spencer gravity (or BCOV theory) on Calabi-Yau manifolds using the formalism for perturbative QFT developed by the first author.

• In this paper, we focus on flat space $\mathbb{C}^d$ for $d$ odd.
• We prove that there exists a unique quantization of the theory coupling BCOV theory and holomorphic Chern-Simons theory with gauge group the supergroup $GL(N \mid N)$.
• We deduce a canonically defined quantization of BCOV theory on its own.