Quantization of open-closed BCOV theory, I

Costello, Kevin; Li, Si

Quantization of open-closed BCOV theory, I

May 25, 2015

105 pages

e-Print:

1505.06703 [hep-th]

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Abstract: (arXiv)

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.

Note:

105 pages

space: Calabi-Yau
quantization
twist
field theory
Chern-Simons term
supersymmetry
supergravity
holomorphic
gravitation

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PERIMETER INSTITUTE FOR THEORETICAL PHYSICS, WATERLOO, ONTARIO CANADA N2L 2Y5 E-mail address: kcostello@perimeterinstitute.ca YAU MATHEMATICAL SCIENCE CENTER, TSINGHUA UNIVERSITY, BEIJING, 100084, CHINA E-mail address: sli@math.tsinghua.edu.cn