SU(N_c -> infinity) Lattice Data and Degrees of Freedom of the QCD string

Lattice simulation data on the critical temperature and long-distance potential, that probe the degrees of freedom of the QCD string, are critically reviewed. It is emphasized that comparison of experimental or SU(N_c) lattice data, at finite number of colors N_c, with free string theory can be misleading due to string interactions. Large-N_c extrapolation of pure lattice gauge theory data, in both 3 and 4 dimensions, indicates that there are more worldsheet degrees of freedom than the purely massless transverse ones of the free Nambu-Goto string. The extra variables are consistent with massive modes of oscillation that effectively contribute like c ~ 1/2 conformal degrees of freedom to highly excited states. As a concrete example, the highly excited spectrum of the Chodos-Thorn relativistic string in 1+1 dimensions is analyzed, where there are no transverse oscillations. It is found that the asymptotic density of states for this model is characteristic of a c=1/2 conformal worldsheet theory. The observations made here should also constrain the backgrounds of holographic string models for QCD.