Vertex algebras and quantum master equation

Abstract

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 that solves the higher genus mirror symmetry conjecture on elliptic curves.

49 pages. References added; statements and arguments improved

References in corpus (4)

• Batalin-Vilkovisky quantization and the algebraic index
• Quantization of open-closed BCOV theory, I
• Effective Batalin-Vilkovisky quantization and geometric applications
• Geometry of Localized Effective Theories, Exact Semi-classical Approximation and the Algebraic Index

Cited by in corpus (4)

• Twisted Supergravity and Koszul Duality: A case study in AdS${}_3$
• Batalin-Vilkovisky quantization and the algebraic index
• Tropical Mirror Symmetry in Dimension One
• Holomorphic field theories and higher algebra