Boundary terms in Nambu-Goto string action

TL;DR

This paper studies the effects of boundary terms in the Nambu-Goto string action, revealing their impact on string dynamics, stability, and the nonlinear nature of Regge trajectories.

Contribution

It demonstrates the significance of boundary terms in string dynamics and analyzes stability and fluctuations of rotating string solutions.

Findings

Boundary terms significantly affect string dynamics.

Fluctuations grow in the most generic solutions.

Regge trajectories are nonlinear.

Abstract

We investigate classical strings defined by the Nambu-Goto action with the boundary term added. We demonstrate that the latter term has a significant bearing on the string dynamics. It is confirmed that new action terms that depend on higher order derivatives of string coordinates cannot be considered as continuous perturbations from the starting string functional. In the case the boundary term reduces to the Gauss-Bonnet term, a stability analysis is performed on the rotating rigid string solution. We determined the most generic solution that the fluctuations grow to. Longitudinal string excitations are found. The Regge trajectories are nonlinear.