Near Hagedorn Dynamics of NS Fivebranes, or A New Universality Class of Coiled Strings

TL;DR

This work analyzes the thermodynamics of NS5‑brane–based Little String Theory (LST) as the temperature approaches the Hagedorn limit, using its holographic CHS throat and near‑extremal NS5‑brane geometry to probe canonical ensemble behavior. It shows that the Hagedorn temperature acts as a limiting, not a phase transition, temperature and that one‑loop corrections produce logarithmic free‑energy terms and a shifted energy–temperature relation, indicating significant deviations from free string thermodynamics. The authors argue that a new universality class of strongly interacting strings—characterized by a strong self‑intersection attraction that drives strings to coil—is required to explain LST thermodynamics, including extensivity in finite volumes and the observed high energy behavior. They support this picture with a matrix/DLCQ perspective and a random‑walk toy model, illustrating how coil formation can naturally arise and potentially explain why Little String Theories exist only in 5+1 dimensions, while outlining directions for further quantitative development.

Abstract

We analyze the thermodynamics of NS 5-branes as the temperature approaches the NS 5-branes' Hagedorn temperature, and conclude that the dynamics of ``Little String Theory'' is a new universality class of interacting strings. First we point out how to vary the temperature of the near extremal solution by taking into account $g_s$ corrections. The Hagedorn temperature is shown to be a limiting temperature for the theory. We then compare the thermodynamics to that of a toy model made of free strings and find basic discrepancies. This suggests a need for a new class of string interactions. We suggest that this new universality class is characterized by a strong attractive self-intersection interaction, which causes strings to be coiled. This model might also explain why ``Little String Theories'' exist in at most 5+1 dimensions.