String excitation energies in SU(N) gauge theories beyond the free-string approximation

In the presence of a static quark--antiquark pair, the spectrum of thelow-lying states in SU($N$) gauge theories is discrete and likely to bedescribed, at large quark separations $r$, by an effective string theory. Theexpansion of the excitation energies in powers of $1/r$, which derives from thelatter, involves an increasing number of unknown couplings that characterizethe string self-interactions. Using open--closed string duality, we show thatthe possible values of the couplings are constrained by a set of algebraicrelations. In particular, the corrections of order $1/r^2$ must vanish, whilethe $1/r^3$ terms (which we work out for the few lowest levels) depend on asingle adjustable coupling only.Comment: Plain TeX source, 27 pages, 2 figures include