Stringy Probe Particle and Force Balance

TL;DR

This paper derives the classical motion of a test string from its action, explores force balance in a specific gravitational setting, and confirms the gyromagnetic ratio and force equilibrium through spin interactions.

Contribution

It provides a direct derivation of the string's equation of motion and demonstrates force balance and gyromagnetic ratio in a multi-soliton background.

Findings

Equation of motion matches known results for extended bodies.

Force balance confirms saturation of Bogomol'nyi bound.

Gyromagnetic ratio g=2 is automatically determined.

Abstract

We directly derive the classical equation of motion, which governs the centre of mass of a test string, from the string action. In a certain case, the equation is basically same as one derived by Papapetrou, Dixon and Wald for a test extended body. We also discuss the force balance using a stringy probe particle for an exact spinning multi-soliton solution of Einstein-Maxwell-Dilaton-Axion theory. It is well known that the force balance condition yields the saturation of the Bogomol'nyi type bound in the lowest order. In the present formulation the gyromagnetic ratio of the stringy probe particle is automatically determined to be $g=2$ which is the same value as the background soliton. As a result we can confirm the force balance via the gravitational spin-spin interaction.