Dual long-distance QCD

We propose an explicit form for the long-range limit of the SU(N) Yang-Mills Lagrangian expressed as a function of the dual (color-electric) vector potentials. While we cannot rigorously derive the Lagrangian, it can be made plausible that it follows from conventional Yang-Mills theory. This dual long-distance QCD Lagrangian has many of the properties of a magnetic superconductor. It has classical solutions corresponding to confined tubes of quantized electric color flux which result from a dual Meissner effect. However, the confining pressure is not produced by a scalar Higgs field, as in ordinary superconductivity, but by a magnetic condensate field which arises naturally from the nonlocal form of the dual Lagrangian. Within the classical approximation, we find the explicit distribution of color fields surrounding a flux tube. Semiclassical quantization around this solution can be expected to yield the QCD string, and the semiclassical expansion parameter is 1/N, where N is the number of colors.