Splitting of folded strings inAdS3

Abstract

In this paper we present semiclassical computations of the splitting of folded spinning strings in ${\mathrm{AdS}}_{3}$, which may be of interest in the context of AdS/CFT duality. We start with a classical closed string and assume that it can split into two closed string fragments, if at a given time two points on it coincide in target space and their velocities agree. First we consider the case of the folded string with large spin. Assuming the formal large-spin approximation of the folded string solution in ${\mathrm{AdS}}_{3}$, we can completely describe the process of splitting: compute the full set of charges and obtain the string solutions describing the evolution of the final states. We find that, in this limit, the world surface does not change in the process and the final states are described by the solutions of the same type as the initial string, i.e. the formal large-spin approximation of the folded string in ${\mathrm{AdS}}_{3}$. Then we consider the general case---splitting of string given by the exact folded string solution. We find the expressions for the charges of the final fragments, the coordinate transformations diagonalizing them and, finally, their energies and spins. Because of the complexity of the initial string profile, we cannot find the solutions describing the evolution of the final fragments, but we can predict their qualitative behavior. We also generalize the results to include circular rotations and windings in ${\mathrm{S}}^{5}$.