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全息禁闭规范理论中的 Hagedorn 温度

On the Hagedorn Temperature in Holographic Confining Gauge Theories

Francesco Bigazzi, Tommaso Canneti, Aldo L. Cotrone

备注：
LaTeX, 37 pages, 1 figure; v3: comments and references added, typos corrected
发表信息：
J. High Energ. Phys. 2023, 34 (2023)
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AI总结：

本文利用全息对偶在弯曲弦背景中计算禁闭规范理论的 Hagedorn 温度，在 $\alpha'$ 领头阶得到其与禁闭弦张力平方根的正比关系。

摘要：

由于态的指数增长而导致的弦配分函数发散，在平直时空中是一个已被充分理解的问题。它可以被解释为在某一温度之上出现快子模式，该温度称为 Hagedorn 温度 $T_H$。在已有文献中，可以找到一些关于将其推广到弯曲时空的直观想法；在弯曲时空中计算极其困难，通常无法给出显式结果。本文针对在与禁闭规范理论全息对偶的弯曲背景上的弦理论，给出了 $\alpha'$ 领头阶下 $T_H$ 的零亏格估计。这是一个特别有趣的情形，因为全息对应将 $T_H$ 等同于对偶规范理论的 Hagedorn 温度。为具体起见，我们聚焦于一个众所周知的背景上的 Type IIA 弦理论，该背景对偶于一个 $SU(N)$ Yang-Mills 理论。所得 Hagedorn 温度结果表明，它正比于 Yang-Mills 禁闭弦张力的平方根。相关系数在领头阶可解析确定，并且与平直空间中 Type II 理论的系数相同。尽管该计算是在一个特定模型中完成的，但其结果可完全一般地应用于具有自上而下全息对偶的禁闭规范理论。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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