String stars in $d\geq 7$

TL;DR

This paper demonstrates the existence of higher-dimensional string star solutions in spacetime dimensions $d\,\geq\,7$, resolving a thermodynamic puzzle related to Horowitz--Polchinski solutions and highlighting their properties near the Hagedorn temperature.

Contribution

It provides explicit constructions and evidence for higher-dimensional string stars in $d\geq 7$, including perturbative solutions in $d=7$ and a new family of solutions in higher dimensions.

Findings

String stars exist in $d\geq 7$ as higher-dimensional counterparts of HP solutions.

In $d=7$, string star size diverges near the Hagedorn temperature.

In $d>7$, string stars have finite size and non-zero free energy at Hagedorn temperature.

Abstract

We raise a thermodynamic puzzle for Horowitz--Polchinski (HP) solutions in the presence of extra compact dimensions and show that it can be resolved by the existence of higher-dimensional string stars. We provide non-trivial evidence for the existence of such string stars in spacetime dimensions $d\geq 7$ as higher-dimensional counterparts of HP solutions. In particular, we explicitly construct string star solutions in $d=7$ that are under perturbative control. In $d>7$, at the Hagedorn temperature, we identify these string stars as a specific normalizable representative of a new one-parameter bounded family of Euclidean solutions which can be under perturbative control. The higher-order $\alpha'$ corrections play a crucial role in our arguments and, as pointed by other works, nullify the previous arguments against the existence of string stars in $d\geq 7$. The higher-dimensional string stars have non-zero free energy at Hagedorn temperature and their mass and free energy are of the same order as those of a string-sized black hole. In $d>7$, these solutions are string sized, but in $d=7$, the size of these solutions diverges as $\sim (T_{\rm H}-T)^{-1/4}$ near the Hagedorn temperature.