A 2-form connection is defined in the space of open string field theory solutions, producing invariant higher holonomies and 3-form curvature potentially corresponding to the B-field.
Quantum Background Independence of Closed String Field Theory
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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.
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Higher Connection in Open String Field Theory
A 2-form connection is defined in the space of open string field theory solutions, producing invariant higher holonomies and 3-form curvature potentially corresponding to the B-field.
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Refines closed string field theory for non-critical backgrounds such as D=26-ε flat space and linear dilaton profiles, constructing the classical BV action at genus zero and extending background independence to first order off the conformal locus.
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