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

TL;DR

This paper investigates the excitation energies of SU(N) gauge theories beyond the free-string approximation, deriving algebraic constraints on string self-interactions and analyzing corrections to the energy spectrum at large quark separations.

Contribution

It introduces a method using open-closed string duality to constrain couplings in the effective string theory of SU(N) gauge theories beyond the free-string approximation.

Findings

Corrections of order 1/r^2 must vanish.

1/r^3 corrections depend on a single coupling.

Derived algebraic relations constrain string self-interactions.

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.