  Conformal block is a function of many variables, usually represented as a
formal series, with coefficients which are certain matrix elements in the
chiral (e.g. Virasoro) algebra. Non-perturbative conformal block is a
multi-valued function, defined globally over the space of dimensions, with many
branches and, perhaps, additional free parameters, not seen at the perturbative
level. We discuss additional complications of non-perturbative description,
caused by the fact that all the best studied examples of conformal blocks lie
at the singularity locus in the moduli space (at divisors of the coefficients
or, simply, at zeroes of the Kac determinant). A typical example is the
Ashkin-Teller point, where at least two naive non-perturbative expressions are
provided by elliptic Dotsenko-Fateev integral and by the celebrated
Zamolodchikov formula in terms of theta-constants, and they are different. The
situation is somewhat similar at the Ising and other minimal model points.
