Finite Temperature Systems of Brane-Antibrane on a Torus

TL;DR

This paper analyzes the thermodynamic behavior of brane-antibrane systems on a torus at finite temperature, revealing phase transitions near the Hagedorn temperature depending on the brane configuration and torus radii.

Contribution

It provides a detailed computation of the finite temperature effective potential for brane-antibrane pairs on a torus, highlighting conditions for phase transitions based on geometry and energy.

Findings

Phase transition near Hagedorn temperature when all radii are string scale and branes are extended.

No phase transition when branes are not extended in all non-compact directions.

Phase transition at high energy for large radii when branes are extended in all non-compact directions.

Abstract

In order to study the thermodynamic properties of brane-antibrane systems in the toroidal background, we compute the finite temperature effective potential of tachyon T in this system on the basis of boundary string field theory. We first consider the case that all the radii of the target space torus are about the string scale. If the Dp-antiDp pair is extended in all the non-compact directions, 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, if the Dp-antiDp pair is not extended in all the non-compact directions, the coefficient is kept negative, and thus a phase transition does not occur. Secondly, we consider the case that some of the radii of the target space torus are much larger than the string scale and investigate the behavior of the potential for each value of the radii and the total energy. If the Dp-antiDp pair is extended in all the non-compact directions, a phase transition occurs for large enough total energy.