• Corpus ID: 119614084

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}
}

• K. Costello, Si Li
• Published 25 May 2015
• Mathematics
• arXiv: High Energy Physics - Theory

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.
We also discuss some conjectural links between BCOV theory in various dimensions and twists of physical theories: in complex dimension $3$ we conjecture a relationship to twists of $(1,0)$ supersymmetric theories and in complex dimension $5$ to a twist of type IIB supergravity.