Superstring entanglement at finite temperature and its Hagedorn behavior

This work demonstrates that the extended density matrix associated with the TFD superstring thermal vacuum exhibits entanglement between string coordinates. The entanglement entropy is calculated and expressed in terms of modular functions, whose properties are then used to study Hagedorn behavior. It is then proven that the entropy is ultraviolet (UV) finite for temperatures below the Hagedorn temperature, and that this UV finiteness depends on the spacetime dimension.