Stringy Horizons II

TL;DR

This paper explores a duality in the spectrum of states around Euclidean black holes in string theory, revealing a transition from oscillator states to wound strings and suggesting a universal horizon behavior.

Contribution

It generalizes the FZZ correspondence to show a duality between oscillator states and wound strings on Euclidean black holes, highlighting a transition in state size with excitation level.

Findings

Normalizable states exhibit duality between oscillator and wound string descriptions.

States change size behavior with excitation level, decreasing then increasing.

Transition between horizon and atmosphere states as excitation varies.

Abstract

We show that the spectrum of normalizable states on a Euclidean SL(2,R)/U(1) black hole exhibits a duality between oscillator states and wound strings. This duality generalizes the FZZ correspondence, which can be thought of as an identification between a normalizable mode of dilaton gravity and a mode of the tachyon with winding number one around the Euclidean time circle. It implies that normalizable states on a large Euclidean black hole have support at widely separated scales. In particular, localized states that are extended over the cap of the cigar (the Euclidian analog of the black hole atmosphere) have a component that is localized near the tip of the cigar (the analog of the stretched horizon). As a consequence of this duality, the states exhibit a transition as a function of radial excitation level. From the perspective of a low energy probe, low lying states are naturally thought of as oscillator states in the black hole atmosphere, while at large excitation level they are naturally described as wound strings. As the excitation level increases, the size of the states first decreases and then increases. This behavior is expected to be a general feature of black hole horizons in string theory.