  Starting from classic work of Feynman on the $\lambda$-point of liquid
Helium, we show that his idea of universal action per particle at the 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 ${}^4$He.
Inversely, one can obtain 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
Feynman-like approach without interaction, estimating the monopole mass at
$T_c$. Then we include 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.
