Consistency of Quantum Background Independence

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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.
23 pages, phyzzx

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