  Low temperature heat transport was used to investigate the ground state of
high-purity single crystals of the lightly-doped cuprate
YBa$_{2}$Cu$_{3}$O$_{6.33}$. Samples were measured on either side of the
superconducting phase boundary, in both zero and applied magnetic field. We
report the observation of delocalized fermionic excitations at zero energy in
the non-superconducting state, which shows that the ground state of underdoped
cuprates is metallic. Its low-energy spectrum appears to be similar to that of
the d-wave superconductor, i.e. nodal. The insulating ground state observed in
underdoped La$_{2-x}$Sr$_{x}$CuO$_4$ is attributed to the competing
spin-density-wave order present in that system.
