  We use Coulomb gas methods to propose an explicit form for the scaling limit
of the partition function of the critical O(n) model on an annulus, with free
boundary conditions, as a function of its modulus. This correctly takes into
account the magnetic charge asymmetry and the decoupling of the null states. It
agrees with an earlier conjecture based on Bethe ansatz and quantum group
symmetry, and with all known results for special values of n. It gives new
formulae for percolation (the probability that a cluster connects the two
opposite boundaries) and for self-avoiding loops (the partition function for a
single loop wrapping non-trivially around the annulus.) The limit n->0 also
gives explicit examples of partition functions in logarithmic conformal field
theory.
