  Emergent quasiparticles with a Dirac dispersion in condensed matter systems
can be described by the Dirac equation for relativistic electrons, in analogy
with Dirac particles in high-energy physics. For example, electrons with a
Dirac dispersion have been intensively studied in electronic systems such as
graphene and topological insulators. However, charge is not a prerequisite for
Dirac fermions, and the emergence of Dirac fermions without charge degree of
freedom has been theoretically predicted to be realized in Dirac quantum spin
liquids. These quasiparticles carry a spin of 1/2 but are charge-neutral, and
so are called spinons. Here we show that the spin excitations of a kagome
antiferromagnet, YCu$_3$(OD)$_6$Br$_2$[Br$_{0.33}$(OD)$_{0.67}$], are conical
with a spin continuum inside, which is consistent with the convolution of two
Dirac spinons. The predictions of a Dirac spin liquid model with a spinon
velocity obtained from the spectral measurements are in agreement with the
low-temperature specific heat of the sample. Our results thus provide spectral
evidence for the Dirac quantum spin liquid state emerging in this kagome
lattice antiferromagnet. However, the locations of the conical spin excitations
differ from those calculated by the nearest neighbor Heisenberg model,
suggesting the Dirac spinons have an unexpected origin.
