Taming open/closed string duality with a Losev trick

TL;DR

This paper develops a string field theory framework for open and closed B-models, demonstrating open/closed string duality through BV quantization and integration over open string fields, and reproduces known shift formulas.

Contribution

It provides a target space string field theory formulation for open and closed B-models and proves open/closed duality via BV quantization and open string field integration.

Findings

Derived target space coefficients for the holomorphic anomaly equation.

Proved open/closed string duality from open string field integration.

Reproduced and extended shift formulas for open/closed duality.

Abstract

A target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual.