  We review some aspects of logarithmic conformal field theories which might
shed some light on the geometrical meaning of logarithmic operators. We
consider an approach, put forward by V. Knizhnik, where computation of
correlation functions on higher genus Riemann surfaces can be replaced by
computations on the sphere under certain circumstances. We show that this
proposal naturally leads to logarithmic conformal field theories, when the
additional vertex operator insertions, which simulate the branch points of a
ramified covering of the sphere, are viewed as dynamical objects in the theory.
  We study the Seiberg-Witten solution of supersymmetric low energy effective
field theory as an example where physically interesting quantities, the periods
of a meromorphic one-form, can effectively be computed within this conformal
field theory setting. We comment on the relation between correlation functions
computed on the plane, but with insertions of twist fields, and torus vacuum
amplitudes.
