Brane-anti-brane systems interaction under tachyon condensation

The interaction between a parallel brane-anti-brane and brane-anti-brane is investigated by regarding the brane-anti-brane pair as a kink or anti-kink type tachyon condensed state. As the kink-type tachyon condensed state is known as a non-BPS brane we expand the Lagrangian of tachyon effective field theory to the quadratic order in the off-diagonal fluctuation and then use the zeta-function regularization and Schwinger perturbative formula to evaluate the interaction within a kink-kink or a kink-anti-kink. The results show that while the kink and kink has repulsive force the kink and anti-kink has attractive force and may annihilate by each other. We, therefore, evaluate the free energy at finite temperature and determine the critical temperature above which the stable state of kink-anti-kink system may be found.