Abstract
We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on boundary condition changing fields. Special care is devoted to the general case when nontrivial multiplicities arise upon defect action. Surprisingly the fusion algebra of defects is realized on open string fields only up to a (star algebra) isomorphism.
Highlights
We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions
Besides the intrinsic importance of the classification of open string field theory (OSFT) solutions, this program can potentially help in the discovery of new D-brane systems, by encoding new world-sheet boundary conditions into the gauge invariant content of OSFT solutions [10, 20, 21]
In this paper, starting from CFT topological defects, we have built new operators acting on the open string star algebra, and we have used them to generate new solutions in OSFT
Summary
In the past 16 years there has been quite a lot of progress in charting out the space of possible solutions of the classical equations of motion of open string field theory (OSFT) [1] by both numerical [2,3,4,5,6,7,8,9,10,11,12] as well as analytic tools [10, 13,14,15,16,17,18,19,20,21,22,23] by which new exact solutions have been found or analyzed [15, 24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]. From the explicit formula [10] for the boundary state in terms of the OSFT classical solution it follows that applying the defect operator to the open string field results in a boundary state encircled by the defect operator which gives a new consistent boundary state of the kind considered by Graham and Watts [60]. We present two independent derivations of our results, one which is algebraic and which builds on the initial analysis by Graham and Watts [60] and one which is geometric and uses the properties of defect networks in presence of boundaries Both our constructions clearly show that the composition of open topological defect operators follows the fusion rules only up to a similarity transformation whose precise structure is encoded in the Racah symbols. Three short appendices contain further results which are used in the main text
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