Effective string excitation energies

In the presence of a static quark-antiquark pair, the spectrum of the low-lying states in SU(N) gauge theories is discrete and likely to be described, at large quark separations r, by an effective string theory. The expansion of the excitation energies in powers of 1/r, which derives from the latter, involves an increasing number of unknown couplings that characterize the string self-interactions. Using open-closed string duality, we show that the possible values of the couplings are constrained by a set of algebraic relations. In particular, the corrections of order 1/r 2 must vanish, while the 1/r 3 terms (which we work out for the few lowest levels) depend on a single adjustable coupling only