String stars in d ≥ 7

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 ≥ 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 α^′ 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 ≥ 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 ∼ (T_H − T)^−1/4 near the Hagedorn temperature.