Bosonic boundary states at finite temperature are constructed as solutions of boundary conditions at $T\ne 0$ for bosonic open strings with a constant gauge field $F_{\mathrm{ab}}$ coupled to the boundary. The construction is done in the framework of thermo field dynamics where a thermal Bogoliubov transformation maps states and operators to finite temperature. Boundary states are given in terms of states from the direct product space between the Fock space of the closed string and another identical copy of it. By analogy with zero temperature, the boundary states have the interpretation of $\mathrm{D}p$-branes at finite temperature. The boundary conditions admit two different solutions. The entropy of the closed string in a $\mathrm{D}p$-brane state is computed and analyzed. It is interpreted as the entropy of the $\mathrm{D}p$-brane at finite temperature.

• Received 10 May 2001

DOI:https://doi.org/10.1103/PhysRevD.64.086005