Brane-Antibrane at Finite Temperature in the Framework of Thermo Field Dynamics

Previously we have investigated the thermodynamical properties of D-brane--anti-D-brane pairs by calculating the one-loop free energy and the finite temperature effective action in the framework of Matsubara formalism. This calculation is based on boundary string field theory, and we have a problem of a choice of Weyl factors on the two boundaries of one-loop open string world-sheet. We have chosen one of them and compute the one-loop free energy. In this paper, we derive the mass spectrum of open strings on a D-brane--anti-D-brane pair supposing that the world-sheet is a strip, and compute the thermal vacuum state, free energy and the partition function for a single open string in the framework of thermo field dynamics. From this we can reproduce the free energy for multiple strings in the case of Matsubara method. This fact reinforces our argument of the choice of the Weyl factors in the case of Matsubara formalism.