Open strings with topologically inspired boundary conditions

TL;DR

This paper investigates how topologically inspired boundary terms, like the Gauss-Bonnet action and Chern number, modify boundary conditions in open string theories without altering their equations of motion.

Contribution

It introduces a general class of topological boundary corrections to open string actions and analyzes their effects on boundary conditions.

Findings

Boundary conditions are modified by topological terms.

Topological corrections do not affect equations of motion.

Implications for string boundary dynamics and topological invariants.

Abstract

We consider an open string described by an action of the Dirac-Nambu-Goto type with topological corrections which affect the boundary conditions but not the equations of motion. The most general addition of this kind is a sum of the Gauss-Bonnet action and the first Chern number (when the background spacetime dimension is four) of the normal bundle to the string worldsheet. We examine the modification introduced by such terms in the boundary conditions at the ends of the string.