Flux Tube Spectra from Approximate Integrability at Low Energies

We provide a detailed introduction to a method we recently proposed for calculating the spectrum of excitations of effective strings such as QCD flux tubes. The method relies on the approximate integrability of the low-energy effective theory describing the flux tube excitations and is based on the thermodynamic Bethe ansatz. The approximate integrability is a consequence of the Lorentz symmetry of QCD. For excited states, the convergence of the thermodynamic Bethe ansatz technique is significantly better than that of the traditional perturbative approach. We apply the new technique to the lattice spectra for fundamental flux tubes in gluodynamics in D = 3 + 1 and D = 2 + 1, and to k-strings in gluodynamics in D = 2 + 1. We identify a massive pseudoscalar resonance on the worldsheet of the confining strings in SU(3) gluodynamics in D = 3 + 1, and massive scalar resonances on the worldsheet of k = 2.3 strings in SU(6) gluodynamics in D = 2 + 1.

Note:

44 pages, 19 figures, v2: references added, to appear in special issue of JETP dedicated to Valery Rubakov's 60th birthday

Bethe ansatz: thermodynamical
energy: low
flux tube: excited state
excited state: spectrum
string: confinement
resonance: pseudoscalar
symmetry: Lorentz
resonance: scalar
integrability
quantum chromodynamics

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