Strings on a Cone and Black Hole Entropy

TL;DR

This paper explores string theory on a conical orbifold, revealing connections to black hole entropy and proposing a new duality, with localized tachyons and potential quantum corrections to entropy proportional to horizon area.

Contribution

It introduces a modular invariant string model on a conical orbifold with localized tachyons and suggests a novel duality akin to R to 1/R symmetry.

Findings

String orbifold model is modular invariant.

Tachyons are localized at the cone tip.

Entropy from twisted sectors is proportional to horizon area.

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 ${\scriptstyle R} \rightarrow {1\over R} $ duality.