 Quasi-primary operator

A quasi-primary operator transforms with weights $(h,\tilde{h})$ under global conformal, or Möbius, transformations. A primary operator has this covariance under every locally invertible holomorphic and antiholomorphic coordinate change. In radial quantization, quasi-primary states are annihilated by $L_1,{\tilde{L}}_1$, whereas primary states are annihilated by every positive Virasoro mode. The stress tensor at nonzero central charge is quasi-primary but not primary because its transformation under a general coordinate change includes a Schwarzian term.