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.