Evidence for negative stiffness of QCD flux tubes in the large-N limit of SU(N)

Quarks are held together by color-electric flux tubes between quarks with a finite thickness determined by the dimensionally transmuted coupling constant. Thick tubes must have a finite curvature stiffness, which led by Polyakov and Kleinert to propose their so-called rigid-string model. Contary to their model, and motivated by the properties of a magnetic flux tubes in type-II superconductors, we put forward the hypothesis that QCD flux tubes have a negative stiffness. We set up a new string model with this property and show that it is free of two principal problems of rigid strings — particle states with negative norm and nonexistence of a lowest-energy state — thus making it a better candidate for a string description of quark forces than previous models. Moreover, the new model is shown to have the same high-temperature real×T2-behavior of the string tension as an SU(N) gluon flux tube at large N, whereas that of rigid strings is complex×T2, that of Nambu-Goto strings is iT. We concludeon that large-N flux tubes have a negative rather than a positive bending stiffness.