Abstract
Using integrability we reduce the problem of constructing general classical splitting string solutions on \( \mathbb{R} \) × S 3 to a series of Birkhoff factorization problems. Namely, given any incoming string solution satisfying a necessary self-intersection property at some given instant in time, we use the integrability of the worldsheet σ-model to implicitly construct the pair of outgoing strings resulting from a split. The solution for each outgoing string is expressed recursively through a sequence of dressing transformations with parameters determined by the solutions to Birkhoff factorization problems in an appropriate real form of the loop group of SL 2(\( \mathbb{C} \)).
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ArXiv ePrint: 1105.3868
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Vicedo, B. Splitting strings on integrable backgrounds. J. High Energ. Phys. 2011, 17 (2011). https://doi.org/10.1007/JHEP11(2011)017
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DOI: https://doi.org/10.1007/JHEP11(2011)017