Brane-Antibrane Systems at Finite Temperature and Phase Transition near the Hagedorn Temperature

Abstract

In order to study the thermodynamic properties of brane-antibrane systems, we compute the finite temperature effective potential of tachyon T in this system on the basis of boundary string field theory. At low temperature, the minimum of the potential shifts towards T = 0 as the temperature increases. In the D9-D9 case, the sign of the coefficient of |T | 2 term of the potential changes slightly below the Hagedorn temperature. This means that a phase transition occurs near the Hagedorn temperature. On the other hand, the coefficient is kept negative in the Dp-Dp case with p ≤ 8, and thus a phase transition does not occur. This leads us to the conclusion that only a D9-D9 pair and no other (lower dimensional) braneantibrane pairs are created near the Hagedorn temperature. We also discuss a phase transition in NS9B-NS9B case as a model of the Hagedorn transition of closed strings.As we commented in §4, the calculation based on the canonical ensemble cannot be trusted if the temperature is closed to the Hagedorn temperature. In this appendix, we show that the

Finite temperature systems of brane-antibrane on a torus

“…The conclusion of our previous work is that only the spacetime-filling D9-D9 pair is created near the Hagedorn temperature in the non-compact background [10]. Since the D9-D9 pair always satisfies D + d = 9, it is also created for large enough E in the toroidal background.…”

“…We only show the results for the D + d ≤ 7 case, because we can obtain these results by the similar calculation to the previous work [10]. temperature effective potential is given by 19) for 20) for 21) for D + d = 5, where 22) and 23) for D + d ≤ 4.…”

“…The density of states has been derived from this formula in the case of closed strings [16,17] and in the case of open strings on D-branes [18], and in the case of open strings on the Dp-Dp system [10]. We will apply this method in the case of open strings on the Dp-Dp system in the toroidal background.…”

“…This is the free energy on the non-compact background [10]. Let us generalize this free energy to that in the toroidal background.…”

“…We can evaluate the singular part of the free energy by computing the discontinuity around the singularity like in the previous paper [10]. But let us compute it by using the incomplete Γ function for the later convenience.…”