Splitting strings on integrable backgrounds

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( $$ \mathbb{C} $$ ).