  Non-local twist operators are introduced for the O(n) and Q-state Potts
models in two dimensions which, in the limits n -> 0 (resp. Q -> 1) count the
numbers of self-avoiding loops (resp. percolation clusters) surrounding a given
point. This yields many results, for example the distribution of the number of
percolation clusters which must be crossed to connect a given point to an
infinitely distant boundary. These twist operators correspond to (1,2) in the
Kac classification of conformal field theory, so that their higher-point
correlations, which describe linking numbers around multiple points, may be
computed exactly. As an application we compute the exact value \sqrt 3/2 for
the dimensionless conductivity at the spin Hall transition, as well as the
shape dependence of the mean conductance in an arbitrary simply connected
geometry with two extended edge contacts.
