# Effective Batalin-Vilkovisky quantization and geometric applications

@article{Li2017EffectiveBQ, title={Effective Batalin-Vilkovisky quantization and geometric applications}, author={Si Li}, journal={arXiv: Quantum Algebra}, year={2017} }

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 quantum mechanics and algebraic index, (2) Elliptic curve and higher genus mirror symmetry, (3) Calabi-Yau geometry and integrable hierarchy. This note is an expansion of author's talk at ICCM 2016.

## 6 Citations

### Vertex algebras and quantum master equation

- Mathematics
- 2016

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…

### Dispersionless Integrable Hierarchy via Kodaira–Spencer Gravity

- PhysicsCommunications in Mathematical Physics
- 2020

We explain how dispersionless integrable hierarchy in 2d topological field theory arises from the Kodaira–Spencer gravity (BCOV theory). The infinitely many commuting Hamiltonians are given by the…

### Homotopy transfer for QFT on non-compact manifold with boundary: a case study

- Physics
- 2022

In this work we report a homological perturbation calculation to construct effective theories of topological quantum mechanics on R>0. Such calculation can be regarded as a generalization of Feynman…

### Frobenius manifolds and quantum groups

- Mathematics
- 2017

We introduce an isomonodromic Knizhnik-Zamolodchikov connection with respect to the quantum Stokes matrices, and prove that the semiclassical limit of the KZ type connection gives rise to the…

### Exact renormalization group and effective action: A Batalin–Vilkovisky algebraic formulation

- MathematicsJournal of Mathematical Physics
- 2019

In the present paper, which is a mathematical follow--up of [16] taking inspiration from [11], we present an abstract formulation of exact renormalization group (RG) in the framework of…

### Exact renormalization group in Batalin-Vilkovisky theory

- Physics
- 2017

A bstractIn this paper, inspired by the Costello’s seminal work [11], we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In…

## References

SHOWING 1-10 OF 39 REFERENCES

### Geometry of Batalin-Vilkovisky quantization

- Mathematics
- 1992

The geometry ofP-manifolds (odd symplectic manifolds) andSP-manifolds (P-manifolds provided with a volume element) is studied. A complete classification of these manifolds is given. This…

### The Geometry of the Master Equation and Topological Quantum Field Theory

- Mathematics
- 1997

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,…

### Mirror Symmetry and Elliptic Curves

- Mathematics
- 1995

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…

### Quantization of open-closed BCOV theory, I

- Mathematics
- 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…

### Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem

- Mathematics
- 1983

Fermionic quantization, or Clifford algebra, is combined with pseudodifferential operators to simplify the proof of the Atiyah-Singer index theorem for the Dirac operator on a spin manifold.

### Chiral differential operators via Batalin-Vilkovisky quantization

- Mathematics
- 2016

We show that the local observables of the curved beta gamma system encode the sheaf of chiral differential operators using the machinery of the book "Factorization algebras in quantum field theory",…

### BCOV theory on the elliptic curve and higher genus mirror symmetry

- Mathematics
- 2011

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…

### Closed string field theory: Quantum action and the Batalin-Vilkovisky master equation

- Mathematics, Physics
- 1992

### 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…