Strings on a Cone and Black Hole Entropy

Abstract

String propagation on a cone with deficit angle $2\pi (1-\frac{1}{N})$ is described by constructing a non-compact orbifold of a plane by a $Z_N$ subgroup of rotations. It is modular invariant and has tachyons in the twisted sectors that are localized to the tip of the cone. A possible connection with the quantum corrections to the black hole entropy is outlined. The entropy computed by analytically continuing in N would receive contribution only from the twisted sectors and be naturally proportional to the area of the event horizon. Evidence is presented for a new duality for these orbifolds similar to the $R\to \frac{1}{R}$ duality.

20 pages, harvmac, revised version published in Nucl. Phys. B

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