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arXiv · 2510.17951

A spin on Hagedorn temperatures and string stars

Josef Seitz·Erez Y. Urbach
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Abstract

We discuss the correspondence between highly excited strings and black holes in the presence of angular momentum. At fixed imaginary angular velocity $\nu$, we show that free strings exhibit a Hagedorn instability due to a thermal-winding mode turning tachyonic. This allows us to determine the exact Hagedorn temperature $\beta_H(\nu)$ for bosonic, type II, and heterotic strings. Using the effective field theory for the thermal-winding mode around the $\nu$-dependent background, we find a novel `rotating string star' saddle (perturbatively in the angular velocity) and study its properties. This configuration describes a self-gravitating bound state of highly excited rotating strings. As in the non-rotating case, the saddle is qualitatively shown to interpolate between the rotating strings phase and a rotating black hole. We also comment on the implications of these results for anti-de Sitter space.

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Josef Seitz, Erez Y. Urbach. 2025-10-20. A spin on Hagedorn temperatures and string stars. https://arxiv.org/abs/2510.17951

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