Splitting of folded strings in AdS_3

TL;DR

This paper analyzes the semiclassical splitting of folded spinning strings in AdS_3 within the context of AdS/CFT, providing detailed charge calculations and behavior predictions for the resulting string fragments.

Contribution

It introduces a comprehensive semiclassical framework for string splitting in AdS_3, including large-spin approximations and exact solutions, with extensions to circular rotations and windings.

Findings

In the large-spin limit, the world surface remains unchanged during splitting.

Explicit charge and energy expressions for final string fragments are derived.

Qualitative behavior of fragments is predicted for the exact string solutions.

Abstract

In this paper we present semiclassical computations of the splitting of folded spinning strings in 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 on 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 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 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. Due to 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 S^5.