Dilute monopole gas, magnetic screening and k-tensions in hot gluodynamics

An adjoint multiplet of screened monopoles forming a dilute gas fits very well lattice data at high $T$. There are now seven ratios for k-strings available, checking within a few percent with the prediction $k(N-k)$. The diluteness turns out to be a small parameter for SU(N) gluodynamics, to a good approximation ($1\over N^2$) independent of the value of $N$, and also independent of $T$. This suggests a dilute Bose-Einstein gas, with a BE transition at the deconfinement temperature $T_c$.