Closed-String Tachyons and the Hagedorn Transition in AdS Space

TL;DR

This paper explores the behavior of string gases near the Hagedorn temperature in AdS space, proposing a connection between tachyon condensation, black hole formation, and holographic principles, with implications for string theory decay processes.

Contribution

It introduces a novel perspective linking off-shell RG flow to Euclidean AdS black holes and proposes a boundary entropy concept decreasing along the flow.

Findings

Hagedorn tachyon can be localized in AdS space.

RG flow corresponds to Euclidean AdS black hole formation.

Type 0A string decays into type IIB vacuum via tachyon condensation.

Abstract

We discuss some aspects of the behaviour of a string gas at the Hagedorn temperature from a Euclidean point of view. Using AdS space as an infrared regulator, the Hagedorn tachyon can be effectively quasi-localized and its dynamics controled by a finite energetic balance. We propose that the off-shell RG flow matches to an Euclidean AdS black hole geometry in a generalization of the string/black-hole correspondence principle. The final stage of the RG flow can be interpreted semiclassically as the growth of a cool black hole in a hotter radiation bath. The end-point of the condensation is the large Euclidean AdS black hole, and the part of spacetime behind the horizon has been removed. In the flat-space limit, holography is manifest by the system creating its own transverse screen at infinity. This leads to an argument, based on the energetics of the system, explaining why the non-supersymmetric type 0A string theory decays into the supersymmetric type IIB vacuum. We also suggest a notion of `boundary entropy', the value of which decreases along the line of flow.