Virasoro generator ($L_n=(2\pi i{)}^{-1}\oint dz{z}^{n+1}T(z)$)

Virasoro generators are the contour modes of the holomorphic stress tensor in a two-dimensional conformal field theory. Their commutators are $[L_m,L_n]=(m-n)L_{m+n}+c(m^3-m){\delta }_{m+n,0}/12$. A contour around an operator insertion extracts the corresponding coefficient of its stress-tensor operator product expansion. $L_{-1}$ generates translations, $L_0$ measures holomorphic weight, and all positive generators annihilate a primary state. An independent antiholomorphic copy acts on the other weight.