The Curious Case of an Effective Theory

TL;DR

This paper develops an effective scalar field theory inspired by gluodynamics, revealing classical string solutions with unique degeneracy properties and connections to Abelian QED in certain limits.

Contribution

It introduces a novel effective scalar field theory with classical string solutions and explores its features related to gluodynamics and Abelian QED.

Findings

Identifies two massless particles in the theory, matching Abelian QED.

Finds classical string solutions with degenerate configurations.

Shows all solutions have identical electric fields and string tension.

Abstract

We describe an effective theory of a scalar field, motivated by some features expected in the low energy theory of gluodynamics in 3+1 dimensions. The theory describes two propagating massless particles in a certain limit, which we identify with the Abelian QED limit, and has classical string solutions in the general case. The string solutions are somewhat unusual as they are multiply degenerate due to spontaneous breaking of diffeomorphism invariance. Nevertheless all solutions yield identical electric field and have the same string tension.