Phases of bosonic strings and two dimensional gauge theories

TL;DR

This paper explores how extrinsic curvature and torsion in bosonic strings can be modeled using two-dimensional gauge theories, revealing phases corresponding to open and closed strings, and connecting to SU(2) Yang-Mills theory.

Contribution

It introduces a novel gauge field theory framework for bosonic strings using extrinsic curvature and torsion, linking string phases to gauge symmetry breaking.

Findings

Unbroken gauge symmetry phase corresponds to open strings.

Broken gauge symmetry phase corresponds to closed strings.

Extension to SU(2) Yang-Mills theory provides additional interpretation.

Abstract

We suggest that the extrinsic curvature and torsion of a bosonic string can be employed as variables in a two dimensional Landau-Ginzburg gauge field theory. Their interpretation in terms of the abelian Higgs multiplet leads to two different phases. In the phase with unbroken gauge symmetry the ground state describes open strings while in the phase with broken gauge symmetry the ground state involves closed strings. When we allow for an additional abelian gauge structure along the string, we arrive at an interpretation in terms of the two dimensional SU(2) Yang-Mills theory.