Excited Mesons and Quantization of String Endpoints

TL;DR

This paper investigates the mass spectra of mesons in different string theory backgrounds, revealing distinct behaviors for light and highly excited states, and introduces a new quantization method for open string endpoints.

Contribution

It presents a novel approach to quantize open string endpoints and analyzes meson spectra, highlighting differences between weakly curved backgrounds and generic confining theories.

Findings

Highly excited mesons follow M_n ~ sqrt(n) spectrum.

Light mesons with spin J <= 1 follow M_n ~ n spectrum.

Proposes a semiclassical quantization method for open 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.