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QCD Flux Tube Spectrum from Approximate Integrability

I will describe a new approach to the theory of confining flux tubes in QCD . It relies on the approximate integrability of the low energy theory describing flux tube excitations . Both integrability and the fact that it is only approximate are direct consequences of non-linearly realized Lorentz symmetry. Our method allows for a precise comparison with the lattice simulations that reveals a presence of massive resonances localized on the flux tubes in 4D Yang-Mills as well as on the k-strings in 3D Yang-Mills theories. Intriguingly, in the 4D case the width of the resonance suggests a relation between the QCD strings and a novel non-critical string theory.