Universal Confining Strings: From Compact QED to the Hadron Spectrum

We investigate the description of quark confinement in terms of confining strings or flux tubes. We show that compact QED with a topological $θ$-term, in the dyon condensation phase, is described by a massive two-form field $B_{μν}$ that gives rise to a string theory with an IR Brazovskii-Lifshitz fixed point at strong coupling. This corresponds to a quantum consistent "free string" in (3+1) dimensions, representing the dual of asymptotic freedom in the UV. Contrary to critical strings, which correspond to trivial Gaussian fixed points, this string is stabilized by a finite thickness, determined by the mass of the $B_{μν}$ field, instead of living in a higher-dimensional space. It correspondingly contains a massive world-sheet resonance, in addition to the Nambu-Goto phonons, that improves fitting with data. We compute the confining potential and show that it reproduces a generalized Arvis potential $V(L) = aL \sqrt{1 - c/L^2}$ with running parameters $a(L), c(L)$. We compute the mass difference ratios for the heaviest quarkonium and find 2.5 percent agreement with experiment already at the infrared fixed point. We also compute the intercept of Regge trajectories and find that the thickness of Brazovskii-Lifshitz strings tends to increase it from the Nambu-Goto value $α_0 = 1/12$. Overall, our findings strongly support Polyakov's longstanding conjecture on universality of confining gauge theories in the IR.