Quantum Background Independence of Closed String Field Theory

TL;DR

This paper proves that quantum closed string field theory is locally background independent by constructing a map between nearby conformal theories using advanced algebraic and geometric methods, confirming that different conformal theories are just different states of the same underlying theory.

Contribution

It establishes the local background independence of quantum closed string field theory through a novel geometric and algebraic framework involving BV algebras and string vertices.

Findings

Constructs an antibracket preserving map between state spaces of nearby conformal theories.

Shows that background independence arises from vacuum vertices and the theory space connection.

Provides a geometric construction of the map using BV algebra on Riemann surfaces.

Abstract

We prove local background independence of the complete quantum closed string field theory using the recursion relations for string vertices and the existence of connections in CFT theory space. Indeed, with this data we construct an antibracket preserving map between the state spaces of two nearby conformal theories taking the corresponding string field measures $d\mu e^{2S/\hbar}$ into each other. A geometrical construction of the map is achieved by introducing a Batalin-Vilkovisky (BV) algebra on spaces of Riemann surfaces, together with a map to the BV algebra of string functionals. The conditions of background independence show that the field independent terms of the master action arise from vacuum vertices $\V_{g,0}$, and that the overall $\hbar$-independent normalization of the string field measure involves the theory space connection. Our result puts on firm ground the widely believed statement that string theories built from nearby conformal theories are different states of the same theory.