Strictly speaking, it is possible for a two-dimensional conformal field theory to be local (in the sense of possessing a stress-tensor) while still only exhibiting invariance under the global P S L 2 ( C ) . This turns out to be unique to non-unitary theories; an example is the biharmonic scalar. This property should be viewed as even more special than scale without conformal invariance as it requires T μ μ μ μ to be a total second derivative.