String Thermodynamics in D-Brane Backgrounds

TL;DR

This paper investigates the thermal behavior of string gases in various D-brane backgrounds near the Hagedorn temperature, revealing how dimensionality influences limiting behavior and implications for early universe cosmology.

Contribution

It provides a detailed analysis of the Hagedorn transition in D-brane backgrounds, highlighting the dependence on dimensionality and the effects of thermal contact between systems.

Findings

Non-limiting behavior in canonical ensemble can become limiting in microcanonical ensemble.

Energy tends to flow into open strings on the largest D-branes in thermal contact.

Implications for the stability of high-dimensional Dp-branes in early cosmological scenarios.

Abstract

We discuss the thermal properties of string gases propagating in various D-brane backgrounds in the weak-coupling limit, and at temperatures close to the Hagedorn temperature. We determine, in the canonical ensemble, whether the Hagedorn temperature is limiting or non-limiting. This depends on the dimensionality of the D-brane, and the size of the compact dimensions. We find that in many cases the non-limiting behaviour manifest in the canonical ensemble is modified to a limiting behaviour in the microcanonical ensemble and show that, when there are different systems in thermal contact, the energy flows into open strings on the `limiting' D-branes of largest dimensionality. Such energy densities may eventually exceed the D-brane intrinsic tension. We discuss possible implications of this for the survival of Dp-branes with large values of p in an early cosmological Hagedorn regime. We also discuss the general phase diagram of the interacting theory, as implied by the holographic and black-hole/string correspondence principles.