• Corpus ID: 119708892

Vertex algebras and quantum master equation

@article{Li2016VertexAA,
  title={Vertex algebras and quantum master equation},
  author={Si Li},
  journal={arXiv: Quantum Algebra},
  year={2016}
}
  • Si Li
  • Published 5 December 2016
  • Mathematics
  • arXiv: Quantum Algebra
We study the effective Batalin-Vilkovisky quantization theory for chiral deformation of two dimensional conformal field theories. We establish an exact correspondence between renormalized quantum master equations for effective functionals and Maurer-Cartan equations for chiral vertex operators. The generating functions are proven to have modular property with mild holomorphic anomaly. As an application, we construct an exact solution of quantum B-model (BCOV theory) in complex one dimension… 

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References

SHOWING 1-10 OF 45 REFERENCES

A Path Integral Approach¶to the Kontsevich Quantization Formula

Abstract: We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path

Effective Batalin-Vilkovisky quantization and geometric applications

We explain the effective renormalization method of quantum field theory in the Batalin-Vilkovisky formalism and illustrate its mathematical applications by three geometric examples: (1) Topological

On the B-twisted topological sigma model and Calabi-Yau geometry

We provide a rigorous perturbative quantization of the B-twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps.

Batalin–Vilkovisky quantization and the algebraic index

Mirror Symmetry and Elliptic Curves

I review how recent results in quantum field theory confirm two general predictions of the mirror symmetry program in the special case of elliptic curves: (1) counting functions of holomorphic curves

Solitons : differential equations, symmetries and infinite dimensional algebras

Preface 1. The KdV equation and its symmetries 2. The KdV hierarchy 3. The Hirota equation and vertex operators 4. The calculus of Fermions 5. The Boson-Fermion correspondence 6. Transformation

BCOV theory on the elliptic curve and higher genus mirror symmetry

We develop the quantum Kodaira-Spencer theory on the elliptic curve and establish the corresponding higher genus B-model. We show that the partition functions of the higher genus B-model on the

The Geometry of the Master Equation and Topological Quantum Field Theory

In Batalin–Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QP-manifold,