# Creation of D9-brane--anti-D9-brane Pairs from Hagedorn Transition of Closed Strings

## TL;DR

This paper proposes that D9-brane--anti-D9-brane pairs are generated during the Hagedorn transition of closed strings, supported by calculations of string amplitudes and potential energy behavior near the Hagedorn temperature.

## Contribution

It introduces the conjecture that D-brane pairs form from closed string Hagedorn transition, supported by amplitude calculations and potential energy analysis.

## Key findings

- Cylinder amplitudes approach sphere amplitudes with winding tachyon insertion.
- Potential energy decreases without bound as temperature nears Hagedorn point.
- Open string vacuum becomes the global minimum near the Hagedorn temperature.

## Abstract

It is well known that one-loop free energy of closed strings diverges above the Hagedorn temperature. One explanation for this divergence is that a `winding mode' in the Euclidean time direction becomes tachyonic above the Hagedorn temperature. The Hagedorn transition of closed strings has been proposed as a phase transition via condensation of this winding tachyon. However, we have not known the stable minimum of the potential of this winding tachyon so far. On the other hand, we have previously calculated the finite temperature effective potential of open strings on D-brane--anti-D-brane pairs, and shown that a phase transition occurs near the Hagedorn temperature and D9-brane--anti-D9-brane pairs become stable. In this paper, we present a conjecture that {\it D9-brane--anti-D9-brane pairs are created by the Hagedorn transition of closed strings}, and describe some circumstantial evidences. We compute two types of the cylinder amplitudes of open strings and show that these amplitudes approach to the sphere amplitude of closed strings with two winding tachyon insertion in the closed string vacuum limit together with the Hagedorn temperature limit. We also show that the potential energy at the open string vacuum decreases limitlessly as the temperature approaches to the Hagedorn temperature. It is natural to think that the open string vacuum becomes the global minimum near the Hagedorn temperature.