arXiv 0802.24532008-02hep-th

分离$D_{p-1}$和反$D_{p-1}$膜在有限温度下的相变

Phase Transitions in Separated $D_{p-1}$ and anti-$D_{p-1}$ Branes at Finite Temperature

Vincenzo Calò, Steven Thomas

备注：: 25 pages, 4 figures; Clarifications added to Section 3 concerning winding modes; updated plots of the effective potential in section 4; typos corrected. Version to be published in JHEP
发表信息：: JHEP 0806:093,2008
DOI：: 10.1088/1126-6708/2008/06/093

摘要：

我们考虑平坦空间中的一对平行的${\rm D}_{p-1}$和反${\rm D}_{p-1}$膜，在有限的温度下，沿某个垂直的空间方向具有有限的分离$d$。如果这个空间方向在一个圆上被紧化，那么通过T-对偶，这个系统等价于一个${\rm D}_{p}$ -反${\rm D}_{p} $对缠绕在对偶圆上，在其中一个膜上有一条恒定的威尔逊线$A \approx d $。我们特别关注的$p=9$的情况下，计算该系统的自由能和研究的发生二阶相变的温度和威尔逊线（膜-反膜分离）是不同的。在Wilson线消失的极限下，我们恢复了文献中已有的结果，即快子场T=0的原点处的开弦真空在足够高的温度下是稳定的，在该温度下发生二级相变.对于足够大的Wilson线，我们发现了新的二阶相变，对应于在有限温度和快子场值下快子有效势的两个极小值的存在。熵的论证表明，当系统冷却时，快子很可能会在温度为零时接近无穷大的最小值（即对应于闭弦真空的最小值），而不是在T=0时的最小值（对应于开弦真空）。

英文摘要：

We consider a pair of parallel ${\rm D}_{p-1}$ and anti-${\rm D}_{p-1}$ branes in flat space, with a finite separation $d$ along some perpendicular spatial direction and at finite temperature. If this spatial direction is compactified on a circle then by T-duality, the system is equivalent to a ${\rm D}_{p}$-anti ${\rm D}_{p} $ pair wrapped around the dual circle with a constant Wilson line $A \approx d $ on one of the branes. We focus in particular on the $p=9$ case and compute the free energy of this system and study the occurrence of second order phase transitions as both the temperature and Wilson line (brane-antibrane separation) are varied. In the limit of vanishing Wilson line we recover the previous results obtained in the literature, whereby the open string vacuum at the origin of the tachyon field T=0 is stabilized at sufficiently high temperature at which a second order phase transition occurs. For sufficiently large Wilson line, we find new second order phase transitions corresponding to the existence of two minima in the tachyon effective potential at finite temperature and tachyon field value. Entropic arguments suggest that as the system cools, the tachyon is likely to find itself in the minimum that approaches infinity as the temperature vanishes (i.e. the one corresponding to the closed string vacuum), rather than the minimum at T=0 (corresponding to the open string vacuum).

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