Stability and Symmetry Breaking for Closed String with Massive Point

TL;DR

This paper investigates the stability of closed relativistic strings with a point mass, revealing a critical mass threshold for stability and identifying symmetry breaking phenomena in rotational states.

Contribution

It introduces a stability analysis of rotational states of closed strings with a massive point, showing a critical mass for stability and the occurrence of spontaneous symmetry breaking.

Findings

Rotational states with a massive point are stable if mass exceeds critical value

States are unstable below the critical mass, indicating symmetry breaking

Other rotational motions are found to be stable

Abstract

The closed relativistic string carrying a point-like mass in the space with nontrivial geometry is considered. For rotational states of this system (resulting in non-trivial Regge trajectories) the stability problem is solved. It was shown that rotations of the folded string with the massive point placed at the rotational center are stable (with respect to small disturbances) if the mass exceeds some critical value: $m>m_{cr}$. But these rotational states are unstable in the opposite case $m<m_{cr}$. We can treat this effect as the spontaneous symmetry breaking for the string state. Other classes of rotational motions of this system have appeared to be stable. These results were obtained both in numerical experiments and the analytical investigation of small disturbances for the rotational states.