Semiclassical quantization of effective string theory and Regge trajectories

We begin with an effective string theory for long distance QCD, and evaluate the semiclassical expansion of this theory about a classical rotating string solution, taking into account the dynamics of the boundary of the string. 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 string approach zero. The theory is then conformally invariant in any spacetime dimension D. For $D=26\mathrm{}$ the 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.