Analytic Estimate of the Order Parameter for Magnetic Charge Condensation in Qcd

A possible mechanism for confinement of color is Dual Superconductivity of the Vacuum 1 2 3. The idea is that magnetic charges condense in the vacuum : the chromoelectric field acting between a q− q̄ pair is channeled by dual Meissner effect into flux tubes with energy proportional to the distance. Flux tubes are indeed observed in lattice simulations , and the corresponding field configurations are consistent with expectations 4. An order parameter 〈μ〉 has been defined 5 6 7 8 9 which is the vacuum expectation value of a magnetically charged operator μ. Numerical simulations show that 〈μ〉 6 = 0 in the confined phase , signaling Higgs breaking of magnetic U(1) symmetry , 〈μ〉 = 0 in the deconfined phase. Deconfinement is an order-disorder phase transition. For SU(N) gauge group there exist (N− 1) magnetic charges 10and the corresponding operators μ, (a = 1, .., N−1) can be written as