  The current algebra for gauge theories like QCD at finite temperature and
density is studied. We start considering, the massless Thirring model at finite
temperature and density, finding an explicit expression for the current
algebra. The central charge only depends on the coupling constant and there are
not new effects due to temperature and density. From this calculation, we argue
how to compute the central charge for $QCD_4$ and we argue why the central
charge in four dimensions could be modified by finite temperature and density.
