• Corpus ID: 237346913

Large $N$ phenomena and quantization of the Loday-Quillen-Tsygan theorem

@inproceedings{Ginot2021LargeP,
  title={Large \$N\$ phenomena and quantization of the Loday-Quillen-Tsygan theorem},
  author={Gr{\'e}gory Ginot and Owen Gwilliam and Alastair Hamilton and Mahmoud Zeinalian},
  year={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 that setting. Matrix integrals offer a key example: we demonstrate how this formalism leads to a recurrence relation that in principle allows us to compute all multi-point correlation functions. We also explain how the Harer-Zagier relations may be expressed in terms of this noncommutative geometry… 
1 Citations
A homological approach to the Gaussian Unitary Ensemble
We study the Gaussian Unitary Ensemble (GUE) using noncommutative geometry and the homological framework of the Batalin-Vilkovisky (BV) formalism. Coefficients of the correlation functions in the GUE

References

SHOWING 1-10 OF 47 REFERENCES
Quantization of open-closed BCOV theory, I
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
Derived Representation Schemes and Noncommutative Geometry
Some 15 years ago M. Kontsevich and A. Rosenberg [KR] proposed a heuristic principle according to which the family of schemes ${Rep_n(A)}$ parametrizing the finite-dimensional represen- tations of a
The partition function of a topological field theory
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∞
Topological conformal field theories and Calabi–Yau categories
Anomaly cancellation in the topological string
  • K. Costello, Si Li
  • Mathematics
    Advances 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
Classes on Compactifications of the Moduli Space of Curves Through Solutions to the Quantum Master Equation
In this paper we describe a construction which produces classes in compactifications of the moduli space of curves. This construction extends a construction of Kontsevich which produces classes in
Algebraic Structure of Yang-Mills Theory
In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with [15] and devoted to maximally supersymmetric
Dual Feynman transform for modular operads
We introduce and study the notion of a dual Feynman transform of a modular operad. This generalizes and gives a conceptual explanation of Kontsevich's dual construction producing graph cohomology
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