From QCD to Dual Superconductivity to Effective String Theory

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 use the semiclassical expansion of this effective string theory about a classical rotating string solution in any spacetime dimension D to obtain the semiclassical meson energy spectrum. We argue that the experimental data on Regge trajectories along with numerical simulations of the heavy quark potentials provide good evidence for an effective string description of long distance QCD.Comment: Talk given at the 5th International Conference on Quark Confinement and the Hadron Spectrum, Gargnano, Italy, September 200

A universal solution

The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations derivable from an arbitrary Lagrangian which is homogeneous of weight one in the field derivatives. This result is extended to many fields. The imposition of Lorentz invariance makes such Lagrangians unique, and equivalent to the Companion Lagrangians introduced in [baker].Comment: arxiv version is already officia

Effective String Theory of Vortices and Regge Trajectories

Starting from a field theory containing classical vortex solutions, we obtain an effective string theory of these vortices as a path integral over the two transverse degrees of freedom of the string. We carry out a semiclassical expansion of this effective theory, and use it to obtain corrections to Regge trajectories due to string fluctuations.Comment: 27 pages, revtex, 3 figures, corrected an error with the cutoff in appendix E (was previously D), added more discussion of Fig. 3, moved some material in section 9 to a new appendi