论文标题
在全息限制理论的Hagedorn温度下
On the Hagedorn Temperature in Holographic Confining Gauge Theories
论文作者
论文摘要
由于状态的指数增长而导致的字符串分区函数的差异是扁平时空中的一个很好的问题。它可以解释为在一定温度以上的鼠标模式的外观，称为Hagedorn温度$ T_H $。在文献中，人们可以找到有关其对弯曲空间的概括的一些直觉，其中计算非常硬，并且无法提供明确的结果。在本文中，我们在$α'$中以$α$的领先顺序提出了零元的估计，用于弯曲背景的字符串理论在弯曲的背景上偶发到限制规格理论。这是一个特别有趣的案例，因为全息光的信件将$ t_h $等同于双仪理论的Hagedorn温度。为了具体关系，我们将重点介绍IIA类弦理论，以$ su（n）$ yang-mills理论的众所周知的背景双重。事实证明，所得的HageDorn温度与延绳张力的杨利尔的平方根成正比。相关系数通过分析确定的领先顺序确定，与平面空间中II型理论的系数相同。尽管计算是在特定模型中执行的，但结果完全普遍于将仪表理论与自上而下的全息二元相限制。
The divergence of the string partition function due to the exponential growth of states is a well-understood issue in flat spacetime. It can be interpreted as the appearance of tachyon modes above a certain temperature, known as the Hagedorn temperature $T_H$. In the literature, one can find some intuitions about its generalization to curved spacetimes, where computations are extremely hard and explicit results cannot be provided in general. In this paper, we present a genus-zero estimate of $T_H$, at leading order in $α'$, for string theories on curved backgrounds holographically dual to confining gauge theories. This is a particularly interesting case, since the holographic correspondence equates $T_H$ with the Hagedorn temperature of the dual gauge theories. For concreteness we focus on Type IIA string theory on a well known background dual to an $SU(N)$ Yang-Mills theory. The resulting Hagedorn temperature turns out to be proportional to the square root of the Yang-Mills confining string tension. The related coefficient, which at leading order is analytically determined, is the same as the one for Type II theories in flat space. While the calculation is performed in a specific model, the result applies in full generality to confining gauge theories with a top-down holographic dual.
