  The Kitaev quantum spin liquid (KSL) is a theoretically predicted state of
matter whose fractionalized quasiparticles are distinct from bosonic magnons,
the fundamental excitation in ordered magnets. The layered honeycomb
antiferromagnet $\alpha$-RuCl$_3$ is a KSL candidate material, as it can be
driven to a magnetically disordered phase by application of an in-plane
magnetic field, with $H_c \sim 7$ T. Here we report a detailed characterization
of the magnetic excitation spectrum of this material by high-resolution
time-domain terahertz (THz) spectroscopy. We observe two sharp magnon
resonances whose frequencies and amplitudes exhibit a discontinuity as a
function of applied magnetic field, as well as two broader peaks at higher
energy. Below the N\'eel temperature, we find that linear spin wave theory can
account for all of these essential features of the spectra when a
$C_3$-breaking distortion of the honeycomb lattice and the presence of
structural domains are taken into account.
