Suppose there is a conformal field theory which has the global conformal symmetry namely $SL(2,R).$ and after central extension it is enhanced to Virasoro algebra with central charge, $c=0$ (also known as Witt algebra). What does this physically signify?
In 2D CFT $c$ has different physical interpretations : it is a measure of degrees of freedom, Weyl anomaly etc. What is the implication of having a CFT with $c=0$?
Edit : I am particularly interested about $D=1$. In this case there are papers (e.g, hep/th 9901139) which says the global conformal symmetry enhances to Virasoro algebra whose central charge, $c=0$.