  In this paper we continue the investigation of the regularity of the
so-called weak $\frac{n}{p}$-harmonic maps in the critical case. These are
critical points of the following nonlocal energy \[
{\mathcal{L}}_s(u)=\int_{\mathbb{R}^n}| ( {-\Delta})^{\frac{s}{2}} u(x)|^p
dx\,, \] where $u\in \dot{H}^{s,p}(\mathbb{R}^n,\mathcal{N})$ and
${\mathcal{N}}\subset\mathbb{R}^N$ is a closed $k$ dimensional smooth manifold
and $s=\frac{n}{p}$. We prove H\"older continuity for such critical points for
$p \leq 2$. For $p > 2$ we obtain the same under an additional Lorentz-space
assumption. The regularity theory is in the two cases based on regularity
results for nonlocal Schr\"odinger systems with an antisymmetric potential.
