  We prove that for antisymmetric vectorfield $\Omega$ with small $L^2$-norm
there exists a gauge $A \in L^\infty \cap \dot{W}^{1/2,2}(\mathbb{R}^1,GL(N))$
such that ${\rm div}_{\frac12} (A\Omega - d_{\frac{1}{2}} A) = 0$. This extends
a celebrated theorem by Rivi\`ere to the nonlocal case and provides
conservation laws for a class of nonlocal equations with antisymmetric
potentials, as well as stability under weak convergence.
