The Maximal Abelian Gauge in SU(N)SU(N) gauge theories and thermal monopoles for N=3N=3

We discuss and propose a proper extension of the Abelian projection based on the Maximal Abelian Gauge to SU(N)SU(N) gauge theories. Based on that, we investigate the properties of thermal Abelian monopoles in the deconfined phase of the SU(3)SU(3) pure gauge theory. Such properties are very similar to those already found for SU(2)SU(2), confirming the relevance of the magnetic component close to TcTc and the possible condensation of thermal monopoles as the deconfinement temperature is crossed from above. Moreover, we study the correlation functions among monopoles related to different U(1)U(1) subgroups, which show interesting features and reveal the presence of non-trivial interactions.