Superconformal ghost correlations on Riemann surfaces

We give a short summary of chiral bosonization on Riemann surfaces, with emphasis on commuting fermions, so-called (β,γ) systems. Employing Fay's trisecant identity a new, fermionic representation for superconformal ghost correlations is found. Especially useful for multi-loop superstring calculations, it completes an earlier proof that the cosmological constant vanishes up to eight loops. (orig.)