Non-unitary observables in the 2d critical Ising model

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We introduce three non-local observables for the two-dimensional Ising model. At criticality, conformal field theory may be used to obtain theoretical predictions for their behavior. These formulae are explicit enough to show that their asymptotics are described by highest weights hpq from the Kac table for c=1/2 distinct from those of the three unitary representations (0, 1/16 and 1/2).