Effective string excitation energies

Abstract

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.