Description
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.
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.