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…
40 Citations
Twisted Supergravity and Koszul Duality: A Case Study in AdS$$_3$$
- MathematicsCommunications in Mathematical Physics
- 2021
In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS$_3\times S^3\times T^4$ and the SCFT (on the moduli space of) the symmetric orbifold theory…
Towards the Finite-$N$ Twisted Holography from the Geometry of Phase Space
- Mathematics
- 2021
: We study ring of functions on the (classical and quantized) phase space of 2 d BF theory with the gauge group GL N coupled to a 1 d quantum mechanics with global symmetry GL K . These functions are…
Large $N$ phenomena and quantization of the Loday-Quillen-Tsygan theorem
- Mathematics
- 2021
We offer a new approach to large N limits using the Batalin-Vilkovisky formalism, both commutative and noncommutative, and we exhibit how the Loday-Quillen-Tsygan Theorem admits BV quantizations in…
Anomaly cancellation in the topological string
- MathematicsAdvances in Theoretical and Mathematical Physics
- 2020
We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira-Spencer gravity. We explain a new anomaly cancellation mechanism at all loops in perturbation theory for…
Twisted supergravity and its quantization
- Physics, Mathematics
- 2016
Twisted supergravity is supergravity in a background where the bosonic ghost field takes a non-zero value. This is the supergravity counterpart of the familiar concept of twisting supersymmetric…
Quantizing local holomorphic field theories on twistor space
- Mathematics
- 2021
This paper studies a class of four-dimensional quantum field theories which arise by quantizing local holomorphic field theories on twistor space. These theories have some remarkable properties: in…
Holography and Koszul duality: the example of the $M2$ brane
- Mathematics
- 2017
Si Li and author suggested in that, in some cases, the AdS/CFT correspondence can be formulated in terms of the algebraic operation of Koszul duality. In this paper this suggestion is checked…
Holomorphic Poisson Field Theories
- Mathematics
- 2020
We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of…
Twisted eleven-dimensional supergravity
- Mathematics
- 2021
We construct a fully interacting holomorphic/topological theory in eleven dimensions that is defined on products of Calabi–Yau fivefolds with real one-manifolds. The theory describes a particular…
On Cohomological Algebras in Supersymmetric Quantum Field Theories
- Mathematics, Physics
- 2019
In this thesis we compute certain supersymmetric subsectors of the algebra of observables in some Quantum Field Theories (QFTs) and demonstrate an application of such computation in checking an…
References
SHOWING 1-10 OF 24 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.-…