Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 101, 17 pages      arXiv:1212.4234
Contribution to the Special Issue “Mirror Symmetry and Related Topics”

Renormalization Method and Mirror Symmetry

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

Received May 07, 2012, in final form December 13, 2012; Published online December 18, 2012

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.

Key words: BCOV; Calabi-Yau; renormalization; mirror symmetry.

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