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String thermodynamics in and out of equilibrium: Boltzmann equations and random walks

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jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe revisit the study of string theory close to the Hagedorn temperature with the aim towards cosmological applications. We consider interactions of open and closed strings in a gas of Djats:italicp</jats:italic>-branes, and/or one isolated Djats:italicp</jats:italic>-brane, in an arbitrary number jats:italicd</jats:italic> of flat non-compact dimensions and general compact dimensions. Leading order string perturbation theory is used to obtain the basic interaction rates in a flat background, which are shown to be consistent with the random walk picture of highly excited strings that should apply in more general backgrounds. Using the random walk interpretation we infer the structure of more general semi-inclusive string scattering rates and then write down the corresponding Boltzmann equations describing ensembles of highly excited closed and open strings. We organise the interaction terms in Boltzmann equations so that detailed balance becomes manifest. We obtain the equilibrium solutions and show that they reduce to previously computed solutions for jats:italicd</jats:italic> = 0. We further study the behaviour of non-equilibrium fluctuations and find explicit analytic expressions for the equilibration rates (and for the number of open strings in jats:italicd</jats:italic> = 0). Potential implications for an early universe with strings at high temperatures are outlined.</jats:p>


Acknowledgements: We would like to thank Shanta de Alwis, Sebastián Céspedes, Ed Copeland, Amrita Ghosh, Tuhin Ghosh, Chris Hughes, Rishi Mouland, Mario Ramos Hamud, Lárus Thorlacius, David Tong and Yoav Zigdon for stimulating discussions. FM is funded by a UKRI/EPSRC Stephen Hawking fellowship, grant reference EP/T017279/1, partially supported by the STFC consolidated grant ST/P000681/1 and funded by a G-Research grant for postdocs in quantitative fields. The work of FQ has been partially supported by STFC consolidated grants ST/P000681/1, ST/T000694/1. The work of GV has been partially supported by STFC consolidated grant ST/T000694/1. The work of ARF was supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant program, grant 2020-00054. The work of RM has been supported by a fellowship grant from INFN projects ST&FI “String Theory And Fundamental Interactions” and GAST “Gauge And String Theories”.


4902 Mathematical Physics, 5107 Particle and High Energy Physics, 49 Mathematical Sciences, 51 Physical Sciences

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Journal of High Energy Physics

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Springer Science and Business Media LLC
Science and Technology Facilities Council (ST/P000681/1)
STFC (ST/T000694/1)