Effective String Theory of Vortices and Regge Trajectories of Hybrid Mesons with Zero Mass Quarks

We show how a field theory containing classical vortex solutions can be expressed as an effective string theory of long distance QCD describing the two transverse oscillations of the string. We use the semiclassical expansion of this effective string theory about a classical rotating string solution to obtain Regge trajectories for mesons with zero mass quarks. The first semiclassical correction adds the constant 1/12 to the classical Regge formula for the angular momentum of mesons on the leading Regge trajectory. In D spacetime dimensions, this additive constant is (D − 2)/24. The excited states of the rotating string give rise to daughter Regge trajectories determining the spectrum of hybrid mesons.