  We prove the regularity of weak 1/2-harmonic maps from the real line into a
sphere. The key point in our result is first a formulation of the 1/2-harmonic
map equation in the form of a non-local linear Schr\"odinger type equation with
a 3-terms commutators in the right-hand-side . We then establish a sharp
estimate for these 3-commutators.
