  We consider critical points of the energy $E(v) := \int_{\mathbb{R}^n}
|\nabla^s v|^{\frac{n}{s}}$, where $v$ maps locally into the sphere or $SO(N)$,
and $\nabla^s = (\partial_1^s,\ldots,\partial_n^s)$ is the formal fractional
gradient, i.e. $\partial_\alpha^s$ is a composition of the fractional laplacian
with the $\alpha$-th Riesz transform. We show that critical points of this
energy are H\"older continuous.
  As a special case, for $s = 1$, we obtain a new, more stable proof of Fuchs
and Strzelecki's regularity result of $n$-harmonic maps into the sphere, which
is interesting on its own.
