Quantization of open-closed BCOV theory, I

Abstract

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.

105 pages

References in corpus (2)

• On the Classification of Topological Field Theories
• SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry

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