>>14245387I am already aware of other classical field theories which correspond to representations of the Virasoro algebra; one example is Liouville field theory in which - there is a paper by Gervais and Neveu for example. The idea is that the Virasoro generators can do something like act on the modes of the classical field theory, and you'll wind up with a classical field theory which has nothing quantum but has a very nice structure.
Ok, if this is too tricky a question, maybe I can take it a different way in case someone can answer this one:
can we consider c-number functions as being like primary fields of conformal dimension ? They should certainly have zero spin at least
