Open String Thermodynamics and D-Branes

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, $4π^{2}α^{'}/β$. On the contrary, for the $SO(N)$, type-I superstring the dual temperature is given by $β$-duality, $2π^{2}α^{'}/β$. 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.