Factorization Conjecture and the Open/Closed String Correspondence

TL;DR

This paper provides evidence for the factorization of world-sheet path integrals in 2D conformal field theories, linking background shifts in closed strings to boundary deformations in open string field theory, with proofs in specific models.

Contribution

It introduces a factorization conjecture for 2D CFT path integrals and proves it for WZW models, connecting closed and open string backgrounds.

Findings

Path integrals factorize into bulk and boundary parts.

Shift in closed string backgrounds corresponds to boundary deformations.

Proof of factorization in WZW models.

Abstract

We present evidence for the factorization of the world-sheet path integrals for 2d conformal field theories on the disk into bulk and boundary contributions. This factorization is then used to reinterpret a shift in closed string backgrounds in terms of boundary deformations in background independent open string field theory. We give a proof of the factorization conjecture in the cases where the background is represented by WZW and related models.