Confining ensemble of dyons

Abstract

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 (supersymmetric) 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 estimated ratio of the critical temperature to the square root of the string tension is in excellent agreement with the lattice data.