We develop the effective Batalin-Vilkovisky quantization theory for chiral deformation of 2-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. As an application, we explain a universal approach to KdV type integrable hierarchies via B-twisted topological string field theory. This leads to an exact solution of quantum B-model (BCOV theory) in complex one dimension that solves the higher genus mirror symmetry conjecture on elliptic curves.
This video is part of Harvard University‘s conference JDG 2017.
