  Quantum entanglement marks a definitive feature of topological states.
However, the entanglement spectrum remains insufficiently explored for
topological states without a bulk energy gap. Using a combination of field
theory and numerical techniques, we accurately calculate and analyze the
entanglement spectrum of gapless symmetry protected topological states in one
dimension. We highlight that the universal entanglement spectrum not only
encodes the nontrivial edge degeneracy, generalizing the Li-Haldane conjecture
to gapless topological states, but also contains the operator content of the
underlying boundary conformal field theory. This implies that the bulk wave
function can act as a fingerprint of both quantum criticality and topology in
gapless symmetry protected topological states. We also identify a symmetry
enriched conformal boundary condition that goes beyond the conventional
conformal boundary condition.
