Renormalization Method and Mirror Symmetry

TL;DR

This paper explores the construction of higher genus B-models from BCOV theory, utilizing renormalization and mirror symmetry concepts to connect physics and geometry.

Contribution

It introduces a novel approach to higher genus B-model construction using renormalization techniques and clarifies the role of Virasoro constraints in this context.

Findings

Givental's symplectic formalism applied to B-model geometry

Fock space construction via gauge theory renormalization

Physics interpretation of Virasoro constraints

Abstract

This is a brief summary of our works [arXiv:1112.4063, arXiv:1201.4501] on constructing higher genus B-model from perturbative quantization of BCOV theory. We analyze Givental's symplectic loop space formalism in the context of B-model geometry on Calabi-Yau manifolds, and explain the Fock space construction via the renormalization techniques of gauge theory. We also give a physics interpretation of the Virasoro constraints as the symmetry of the classical BCOV action functional, and discuss the Virasoro constraints in the quantum theory.