= Worldsheet conformal Killing group
The worldsheet conformal Killing group is the connected residual group of conformal automorphisms of the chosen compact <Riemann surface>. Its infinitesimal vectors satisfy the <Conformal Killing equation>, or $P_1v=0$ for the <worldsheet diffeomorphism ghost operator>. Its complex dimensions are three on a sphere, one on a torus, and zero for <genus> at least two. The sphere group consists of <Möbius transformations>, while the torus's connected group is translation. Additional discrete automorphisms are handled by the moduli quotient rather than counted as continuous zero modes.
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