Excited Mesons and Quantization of String Endpoints

Abstract

We argue that those field theories containing mesons that are dual to weakly curved string backgrounds are non-generic. The spectrum of highly excited mesons in confining field theories behaves as M_n ~ \sqrt{n} (where n is the radial excitation number), as does the spectrum of the dual mesons described by open strings ending on probe D branes. However, in the weakly coupled backgrounds, we show that the sector of (light) mesons with spin J <= 1, dual to the brane fluctuations, behaves as M_n ~ n, for confining and non--confining theories alike. In order to perform the analysis we suggest a method of quantization of the open string endpoints, and rely heavily on the semiclassical, or WKB, approximation.