We construct the integration measure over the moduli space of an
arbitrary number of N kinds of dyons of the pure SU(N) gauge theory
at finite temperatures. The ensemble of dyons governed by the measure
is mathematically described by a 3-dimensional quantum field
theory that is exactly solvable and is remarkable for a number
of striking features:
1) The free energy has the minimum corresponding to the zero average
Polyakov line, as expected in the confining phase;
2) The correlation function of two Polyakov lines exhibits a linear
potential between static quarks in any N-ality non-zero representation,
with a calculable string tension roughly independent of temperature;
3) The average spatial Wilson loop falls off exponentially with its
area and the same string tension;
4) At a critical temperature the ensemble of dyons rearranges and
de-confines.
5) The calculated ratio of the critical temperature to the square root
of the string tension is in excellent agreement with the lattice data
for any N.
