  We obtain a uniqueness result for the half-wave maps equation in dimension $d
\geq 3$ in the natural energy class with $\mathbb{H}^2$ target. We first
reformulate the half-wave maps equation into a wave maps equation, then
isometrically embed $\mathbb{H}^2$ into some $\mathbb{R}^m$ using the Nash
embedding, and then use a Gr\"{o}nwall's argument.
