Confining strings, axions and glueballs in the planar limit

Abstract

We present recent results on the spectrum of a confining flux-tube that is closed around a spatial torus as a function of its length as well as the spectrum of glueballs. The extraction of the spectra has been realized by simulating four dimensional 𝑆𝑈 ( 𝑁 ) gauge theories and performing measurements using lattice techniques. Regarding flux-tubes, we have performed calculations for 𝑁 = 3 , 5 , 6 and for various values of spin, parity and longitudinal momentum. Long flux-tubes can be thought of as infinitesimally thin strings; hence their spectrum is expected to be described by an effective string theory. Furthermore, the flux-tube’s internal structure makes possible the existence of massive states in addition to string modes. Our calculations demonstrate that although most states exhibit a spectrum which can be approximated adequately by Nambu-Goto there is strong evidence for the existence of a massive axion on the world-sheet of the QCD flux-tube as well as a bound state of two such axions. Regarding glueballs, we extracted spectra from 𝑁 = 2 to 𝑁 = 12 which enables us to extrapolate to 𝑁 = ∞ . Our main aim was to calculate the lightest glueball masses for all different configurations of the quantum numbers of spin, parity and charge conjugation. This provides a major update on the spectrum of glueballs in the planar limit.