Stringy Horizons II

Understand

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).