Bose-Einstein condensation of strongly interacting bosons: From liquid He4 to QCD monopoles

Starting from the classic work of Feynman on the λ point of liquid helium, we show that his idea of universal action per particle at the Bose-Einstein condensation (BEC) transition point is much more robust that it was known before. Using a simple "moving string model" for supercurrent and calculating the action, both semiclassically and numerically, we show that the critical action is the same for noninteracting and strongly interacting systems such as liquid He4. Inversely, one can obtain an accurate dependence of critical temperature on density: one important consequence is that high density (solid) He cannot be a BEC state of He atoms, with upper density accurately matching the observations. We then use this model for the deconfinement phase transition of QCD-like gauge theories, treated as BEC of (color-)magnetic monopoles. We start with a Feynman-like approach without interaction, estimating the monopole mass at Tc. Then we include the monopole's Coulomb repulsion, and formulate a relation between the mass, density and coupling which should be fulfilled at the deconfinement point. We end up proposing various ways to test on the lattice whether it is indeed the BEC point for monopoles.