  It is argued that string theory on the Euclidean version of the Schwarzschild
black hole -- the cigar geometry -- admits a zero mode that is localized at the
tip of the cigar. The presence of this mode implies that in string theory,
unlike in general relativity, the tip of the cigar is a special region. This is
in tension with the Euclidean version of the black hole complementarity
principle. We provide some qualitative arguments that link between this zero
mode and the origin of the black hole entropy and firewall at the horizon.
