Gauge Theory of the String Geodesic Field

TL;DR

This paper introduces a new gauge theory framework for describing string geodesic fields, addressing previous issues and clarifying connections with string currents and gauge potentials, including non-abelian and covariant extensions.

Contribution

It proposes a novel gauge theory for string geodesic fields that overcomes prior limitations and clarifies their relation to string currents and gauge potentials.

Findings

Addresses technical and conceptual problems in string geodesic descriptions.

Clarifies the connection between geodesic fields, string currents, and Kalb-Ramond potentials.

Discusses non-abelian and covariant generalizations.

Abstract

A relativistic string is usually represented by the Nambu-Goto action in terms of the extremal area of a 2-dimensional timelike submanifold of Minkowski space. Alternatively, a family of classical solutions of the string equation of motion can be globally described in terms of the associated geodesic field. In this paper we propose a new gauge theory for the geodesic field of closed and open strings. Our approach solves the technical and conceptual problems affecting previous attempts to describe strings in terms of local field variables. The connection between the geodesic field, the string current and the Kalb-Ramond gauge potential is discussed and clarified. A non-abelian generalization and the generally covariant form of the model are also discussed.