QCD Effective action at high temperature and small chemical potential

We present a construction of an effective Yang-Mills action for QCD, from the expansion of the fermionic determinant in terms of powers of the chemical potential at high temperature, for the case of massless quarks. We analyze this expansion in the perturbative region and find that it gives extra spurious information. We propose for the non-perturbative sector a simplified effective action which, in principle, contains only the relevant information.