A Proof of Local Background Independence of Classical Closed String Field Theory

TL;DR

This paper proves local background independence in classical closed string field theory by explicitly constructing symplectic diffeomorphisms between nearby conformal theories, revealing new string vertices and their geometric relations.

Contribution

It provides a complete proof of background independence by constructing explicit diffeomorphisms and introduces a new family of string vertices satisfying Jacobi identities.

Findings

Constructed symplectic diffeomorphisms between conformal theories.

Discovered a new family of string vertices with Jacobi identities.

Linked string field theory to Riemann surface geometry.

Abstract

We give a complete proof of local background independence of the classical master action for closed strings by constructing explicitly, for any two nearby conformal theories in a CFT theory space, a symplectic diffeomorphism between their state spaces mapping the corresponding non-polynomial string actions into each other. We uncover a new family of string vertices, the lowest of which is a three string vertex satisfying exact Jacobi identities with respect to the original closed string vertices. The homotopies between the two sets of string vertices determine the diffeomorphism establishing background independence. The linear part of the diffeomorphism is implemented by a CFT theory-space connection determined by the off-shell three closed string vertex, showing how string field theory induces a natural interplay between Riemann surface geometry and CFT theory space geometry. (Three figures are contained in a separate tar compressed uuencoded figures file. See the TeX file for instructions for printing the figures.)