Straight-line string with curvature

TL;DR

This paper derives classical and quantum solutions for a relativistic straight-line string with curvature-dependent dynamics, revealing potential nonlinear Regge trajectories and comparing regularization methods with point-like models.

Contribution

It introduces solutions for curved relativistic strings and analyzes their Regge trajectories, extending beyond the traditional Nambu-Goto framework.

Findings

Solutions differ from Nambu-Goto strings by nonlinear Regge trajectories

Regularization methods are discussed and compared with point-like models

Classical and quantum behaviors of curved strings are characterized

Abstract

Classical and quantum solutions for the relativistic straight-line string with arbitrary dependence on the world surface curvature are obtained. They differ from the case of the usual Nambu-Goto interaction by the behaviour of the Regge trajectory which in general can be nonlinear. Regularization of the action is considered and comparison with relativistic point with curvature is made.