  We consider critical curves -- conformally invariant curves that appear at
critical points of two-dimensional statistical mechanical systems. We show how
to describe these curves in terms of the Coulomb gas formalism of conformal
field theory (CFT). We also provide links between this description and the
stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the
long-time limit of stochastic evolution of various SLE observables related to
CFT primary fields. We show how the multifractal spectrum of harmonic measure
and other fractal characteristics of critical curves can be obtained.
