Abstract
Generalizing previous work, we give a new analytic solution in Witten’s open bosonic string field theory which can describe any open string background. The central idea is to use Riemann surface degenerations as a mechanism for taming OPE singularities. This requires leaving the familiar subalgebra of wedge states with insertions, but the payoff is that the solution makes no assumptions about the reference and target D-brane systems, and is therefore truly general. For example, unlike in previous work, the solution can describe time dependent backgrounds and multiple copies of the reference D-brane within the universal sector. The construction also resolves some subtle issues resulting from associativity anomalies, giving a more complete understanding of the relation between the degrees of freedom of different D-brane systems, and a nonperturbative proof of background independence in classical open bosonic string field theory.
Highlights
Background independenceThe formulation of string field theory requires a choice of background
The central idea is to use Riemann surface degenerations as a mechanism for taming OPE singularities. This requires leaving the familiar subalgebra of wedge states with insertions, but the payoff is that the solution makes no assumptions about the reference and target D-brane systems, and is truly general
The construction resolves some subtle issues resulting from associativity anomalies, giving a more complete understanding of the relation between the degrees of freedom of different D-brane systems, and a nonperturbative proof of background independence in classical open bosonic string field theory
Summary
One of the major questions in string field theory is how much of the full landscape of string theory can be seen from the point of view of strings propagating in a given background. Since the intertwining fields represent stretched strings, they must be built from BCFT vacuum states containing boundary condition changing operators. This does not immediately undermine the validity of the solution, since ambiguous products do not appear in essential computations It makes it difficult to meaningfully discuss the relation between open string degrees of freedom on different backgrounds, and, for technical reasons, it complicates generalization to superstring field theory [16]. We can replace this boundary point with an infinitely narrow neck connecting to a finite region of worldsheet, as shown in figure 3 In this region we can place two boundary condition changing operators at separated points, and provided that the resulting 2-point function is equal to 1, we have not changed anything about the identity string field. If the intertwining fields are constructed from flag states, it is clear that the star product ΣΣ will not produce a collision of boundary condition changing operators. This surface can be seen to define a star algebra projector following the arguments given in [17]
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