String Theory Versus Black Hole Complementarity

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.