Splitting strings on integrable backgrounds

TL;DR

This paper develops a method using integrability to explicitly construct the splitting of classical strings on R x S^3, providing a recursive solution for outgoing strings based on initial self-intersecting solutions.

Contribution

It introduces a novel integrability-based recursive approach to construct splitting string solutions on R x S^3, utilizing dressing transformations and Birkhoff factorization.

Findings

Explicit recursive solutions for splitting strings on R x S^3

Use of dressing transformations to generate outgoing strings

Application of Birkhoff factorization in the construction process

Abstract

We use integrability to construct the general classical splitting string solution on R x S^3. 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 sigma-model to 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, the parameters of which are determined by the solutions to Birkhoff factorization problems in an appropriate real form of the loop group of SL(2,C).