Dual Superconductivity, Effective String Theory, and Regge Trajectories

Abstract

We show how an effective field theory of long distance QCD, describing a dual superconductor, can be expressed as an effective string theory of superconducting vortices. We evaluate the semiclassical expansion of this effective string theory about a classical rotating string solution in any spacetime dimension D. We show that, after renormalization, the zero point energy of the string fluctuations remains finite when the masses of the quarks on the ends of the strings approach zero. For D = 26 the semiclassical energy spectrum of the rotating string formally coincides with that of the open string in classical Bosonic string theory. However, its physical origin is different. It is a semiclassical spectrum of an effective string theory valid only for large values of the angular momentum. For D = 4 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. The excited vibrational modes of the rotating string give rise to daughter Regge trajectories determining the spectrum of hybrid mesons.