  Quantum phase transitions out of a symmetry-protected topological (SPT) phase
in (1+1) dimensions into an adjacent, topologically distinct SPT phase
protected by the same symmetry or a trivial gapped phase, are typically
described by a conformal field theory (CFT). At the same time, the low-lying
entanglement spectrum of a gapped phase close to such a quantum critical point
is known(Cho et al., arXiv:1603.04016), very generally, to be universal and
described by (gapless) boundary conformal field theory. Using this connection
we show that symmetry properties of the boundary conditions in boundary CFT can
be used to characterize the symmetry-protected degeneracies of the entanglement
spectrum, a hallmark of non-trivial symmetry-protected topological phases.
Specifically, we show that the relevant boundary CFT is the orbifold of the
quantum critical point with respect to the symmetry group defining the SPT, and
that the boundary states of this orbifold carry a quantum anomaly that
determines the topological class of the SPT. We illustrate this connection
using various characteristic examples such as the time-reversal breaking
"Kitaev chain" superconductor (symmetry class D), the Haldane phase, and the
$\mathbb{Z}_8$ classification of interacting topological superconductors in
symmetry class BDI in (1+1) dimensions.
