Strongly interacting quark gluon plasma, and the critical behaviour of QCD at imaginary mu.

We explore the highly nonperturbative hot region of the QCD phase diagram close to Tc by use of an imaginary chemical potential mu which avoids the sign problem. The simulations use four flavors of staggered fermions and are carried out on a 16^3 x 4 lattice. The number density and the quark number susceptibility are consistent with a critical behavior associated with the transition line in the negative mu^2 half-plane. We compare the analytic continuation of these results with various phenomenological models, none of which provides a satisfactory description of data, a failure on which we make some comments. These results complement and extend the information obtained via the analysis of the susceptibilities evaluated at zero mu, yielding a simple description of the candidate strongly interacting quark-gluon plasma phase. As a byproduct of our analysis we investigate the Polyakov loop and its hermitian conjugate. Our data offer vivid evidence of the importance of the complex nature of the functional integral measure, which results in L(mu) =/= L*(mu) for a real chemical potential .