  We show continuity of solutions $u \in W^{1,n}(B^n,\mathbb{R}^N)$ to the
system \[
  -{\rm div} (|\nabla u|^{n-2} \nabla u) = \Omega \cdot |\nabla u|^{n-2} \nabla
u \] when $\Omega$ is an $L^n$-antisymmetric potential -- and additionally
satisfies a Lorentz-space assumption.
  To obtain our result we study a rotated n-Laplace system \[
  -{\rm div} (Q|\nabla u|^{n-2} \nabla u) = \tilde{\Omega} \cdot |\nabla
u|^{n-2} \nabla u, \] where $Q \in W^{1,n}(B^n,SO(N))$ is the Coulomb gauge
which ensures improved Lorentz-space integrability of $\tilde{\Omega}$. Because
of the matrix-term $Q$, this system does not fall directly into
Kuusi-Mingione's vectorial potential theory. However, we adapt ideas of their
theory together with Iwaniec' stability result to obtain
$L^{(n,\infty)}$-estimates of the gradient of a solution which, by an iteration
argument leads to the regularity of solutions. As a corollary of our argument
we see that $n$-harmonic maps into manifolds are continuous if their gradient
belongs to the Lorentz-space $L^{(n,2)}$ -- which is a trivial and optimal
assumption if $n=2$, and the weakest assumption to date for the regularity of
critical $n$-harmonic maps, without any added differentiability assumption. We
also discuss an application to H systems.
