This article is cited in 3 papers

Renormalization Method and Mirror Symmetry

Si Li

Department of mathematics, Northwestern University, 2033 Sheridan Road, Evanston IL 60208, USA

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.

Keywords: BCOV; Calabi–Yau; renormalization; mirror symmetry.

MSC: 14N35; 58A14; 81T15; 81T70

Received: May 7, 2012; in final form December 13, 2012; Published online December 18, 2012

Language: English

DOI: 10.3842/SIGMA.2012.101

Bibliographic databases:

• 
• 

ArXiv: 1212.4234