String theory at the tip of the cigar

TL;DR

The paper investigates string theory at the tip of the cigar using the exact CFT description of the near-horizon geometry of $k$ near-extremal NS5-branes. It identifies a dilaton zero-mode in the cup and a winding-one tachyon zero-mode at the tip, with the latter dominating in the large-$k$ limit and suggesting localized, string-scale dynamics confined to the tip. The discrete-state partition function is analyzed via modular-invariant constructions and reveals a holomorphic anomaly and non-analytic continuous pieces that prevent a naive decoupling into flat $\mathbb{R}^2$, indicating the tip hosts genuine stringy degrees of freedom. These findings support a universal picture of string theory at the tip of the cigar (STTC) and have potential implications for firewall-like phenomena at black hole horizons, while clarifying how horizon-relevant limits relate to ordinary flat-space string theory.

Abstract

In arXiv:1208.3930 we argued that string theory at the tip of the cigar geometry, obtained by a Wick rotation of the Schwarzschild background, exhibits unexpected features that include degrees of freedom that are confined to the tip. Using the exact worldsheet description of near extremal NS5-branes we further study string theory at the tip of the cigar and find more evidence to its surprising properties.

Figures (2)

• Figure 1: The two components of the zero modes: the dilaton mode is the dominant mode at the cup of the cigar while the tachyon mode dominates the tip of the cigar.
• Figure 2: Bubbles that do not cross the origin do not correspond to a Hawking pair and do not interact with the stringy modes at the origin. Bubbles associated with Hawking particle and its partner do cross the horizon. Their interaction with the stringy modes at the origin is the cause of (\ref{['hp']}).