Deformations of extended objects with edges

TL;DR

This paper develops a gauge covariant framework to analyze fluctuations of relativistic extended objects with edges, revealing complex couplings between bulk and edge fluctuations, exemplified by a string with massive endpoints.

Contribution

It introduces a novel formalism for describing fluctuations of extended objects with edges, accounting for their unique geometrical and gauge properties.

Findings

Fluctuations on edges include components into the bulk, unlike bulk fluctuations.

Couplings between edge and bulk fluctuations are governed by the geometry of the worldsheet.

The formalism is demonstrated on a string with massive endpoints.

Abstract

We present a manifestly gauge covariant description of fluctuations of a relativistic extended object described by the Dirac-Nambu-Goto action with Dirac-Nambu-Goto loaded edges about a given classical solution. Whereas physical fluctuations of the bulk lie normal to its worldsheet, those on the edge possess an additional component directed into the bulk. These fluctuations couple in a non-trivial way involving the underlying geometrical structures associated with the worldsheet of the object and of its edge. We illustrate the formalism using as an example a string with massive point particles attached to its ends.