  We compute one-loop amplitudes in six-dimensional Yang-Mills theory with
half-maximal supersymmetry from first principles: imposing gauge invariance and
locality on an ansatz made from string-theory inspired kinematic building
blocks yields unique expressions for the 3- and 4-point amplitudes. We check
that the results are reproduced in the field-theory limit $\alpha' \rightarrow
0$ of string amplitudes in K3 orbifolds, using simplifications made in a
companion string-theory paper 1603.05262.
