## Vertex algebras, quantum master equation and mirror symmetry

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 be almost holomorphic

modular forms. 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