Consistency of Quantum Background Independence

Abstract

We analyse higher order background independence conditions arising from multiple commutators of background deformations in quantum closed string field theory. The conditions are shown to amount to a vanishing theorem for $Δ_S$ cohomology classes. This holds by virtue of the existence of moduli spaces of higher genus surfaces with two kinds of punctures. Our result is a generalisation of a previous genus zero analysis relevant to the classical theory.