Classical Open String Models in 4-Dim Minkowski Spacetime

TL;DR

This paper explores classical open string models in four-dimensional Minkowski spacetime, focusing on boundary conditions, variational principles, and solutions related to a complex Liouville equation, revealing differences from Nambu-Goto strings.

Contribution

It introduces a revised interpretation of variational problems for second-order derivative Lagrangians and derives a boundary term to control edge conditions and conservation laws.

Findings

Classical open string states correspond to solutions of a complex Liouville equation.

The Liouville potential is finite and constant at boundaries, unlike in Nambu-Goto strings.

The phase of the potential defines topological sectors of solutions.

Abstract

Classical bosonic open string models in fourdimensional Minkowski spacetime are discussed. A special attention is paid to the choice of edge conditions, which can follow consistently from the action principle. We consider lagrangians that can depend on second order derivatives of worldsheet coordinates. A revised interpretation of the variational problem for such theories is given. We derive a general form of a boundary term that can be added to the open string action to control edge conditions and modify conservation laws. An extended boundary problem for minimal surfaces is examined. Following the treatment of this model in the geometric approach, we obtain that classical open string states correspond to solutions of a complex Liouville equation. In contrast to the Nambu-Goto case, the Liouville potential is finite and constant at worldsheet boundaries. The phase part of the potential defines topological sectors of solutions.