# Quantization of open-closed BCOV theory, I

@article{Costello2015QuantizationOO, title={Quantization of open-closed BCOV theory, I}, author={Kevin J. Costello and Si Li}, journal={arXiv: High Energy Physics - Theory}, year={2015} }

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…

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