Phases of bosonic strings and two dimensional gauge theories

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.