# 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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## References

SHOWING 1-10 OF 21 REFERENCES

### Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model

- Mathematics
- 2012

Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed that the B-model of mirror symmetry should be described by a quantum field theory on a Calabi-Yau variety, which they called the Kodaira-Spenser theory…

### Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

- Mathematics
- 1994

We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in…

### The partition function of a topological field theory

- Mathematics
- 2009

This is the sequel to my paper ‘TCFTs and Calabi–Yau categories’, Advances in Mathematics 210 (2007) no. 1, 165–214. Here we extend the results of that paper to construct, for certain Calabi–Yau A∞…

### Gauge theory, topological strings, and S-duality

- Mathematics
- 2004

We offer a derivation of the duality between the topological U(1) gauge theory on a Calabi-Yau 3-fold and the topological A-model on the same manifold. This duality was conjectured recently by Iqbal,…

### Holography for (1,0) theories in six dimensions

- Mathematics
- 2014

A bstractM-theory and string theory predict the existence of many six-dimensional SCFTs. In particular, type IIA brane constructions involving NS5-, D6- and D8-branes conjecturally give rise to a…

### SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry

- Physics, Mathematics
- 2011

### Deformation Quantization of Poisson Manifolds

- Mathematics
- 1997

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the…

### Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I

- Mathematics
- 2006

We develop geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. Geometric approach clarifies several…

### The Floer Memorial Volume

- Mathematics
- 2011

Floer's work on monopoles.- Monopoles on asymptotically flat manifolds.- The configuration space of Yang-Mills-Higgs theory on asymptotically flat manifolds.- Instanton homology and Dehn surgery.-…