Open String Thermodynamics and D-Branes

TL;DR

This paper explores the thermodynamics of open superstrings with D-branes, revealing dual temperature relations and the emergence of Hagedorn singularities linked to tachyon coupling at high temperatures.

Contribution

It introduces finite temperature dualities connecting open string free energy to D-brane self-energy and analyzes the Hagedorn transition in this context.

Findings

Dual temperature relations for open strings and D-branes

Identification of Hagedorn singularity emergence

Connection between tachyon coupling and high-temperature behavior

Abstract

We study the thermodynamics of open superstrings in the presence of $p$-dimensional D-branes. We get some finite temperature dualities relating the one-loop canonical free energy of open strings to the self-energy of D-branes at dual temperature. For the open bosonic string the inverse dual temperature is, as expected, the dual length under T-duality, $4\pi^{2}\alpha^{'}/\beta$. On the contrary, for the $SO(N)$, type-I superstring the dual temperature is given by $\beta$-duality, $2\pi^{2}\alpha^{'}/\beta$. We also study the emergence of the Hagedorn singularity in the dual description as triggered by the coupling of the D-brane to unphysical tachyons as well as the high temperature limit.