Statistics of harmonic measure and winding of critical curves from conformal field theory

Understand

Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle.

• The former is the measure of the jaggedness of the curves while the latter quantifies their tendency to form logarithmic spirals.
• We show how these characteristics are related to local operators of conformal field theory and how they can be computed using conformal invariance of critical systems with central charge $c \leqslant 1$.