论文标题
免费大型$ n $量规理论和字符串的光谱形式
Spectral form factor for free large $N$ gauge theory and strings
论文作者
论文摘要
我们研究了两个不同系统中的光谱形式，即免费的$ n $量规理论和高度激发的弦乐气体。在这两种情况下，在早期光谱形式迅速衰减之后，新的贡献都会出现，从而阻止了光谱形式呈指数级的较小。我们认为只有伴随物质的$ u（n）$量规理论，并使用热载体$ u $的矩阵积分来计算光谱形式。新的马鞍与早期鞍座不同，通过保留中心对称性的某些亚组。对于弦的气体，光谱外形的短时间衰减受状态的连续Hagedorn密度约束，这可以与绕组数字$ \ pm 1 $相关的热绕组模式。我们表明，光谱形式的上升来自其他绕组模式，这些模式也沿时间方向带动动量。我们推测这些字符串模式的经典解决方案的存在，类似于Horowitz-Polchinski解决方案。 我们回顾了黑洞的类似问题。特别是，我们检查了kontsevich-segal标准在复杂的黑洞上有助于光谱形式。在规范的集合数量$ z（β+it）$中，黑洞以$ t \ sim \ Mathcal {o}（β）$不允许。避免这种情况的一种方法是考虑黑洞可允许的微型典型合奏。
We investigate the spectral form factor in two different systems, free large $N$ gauge theories and highly excited string gas. In both cases, after a rapid decay of the spectral form factor at early time, new contributions come in, preventing the spectral form factor from ever becoming exponentially small. We consider $U(N)$ gauge theories with only adjoint matter and compute the spectral form factor using a matrix integral of the thermal holonomy $U$. The new saddles differ from the early time saddle by preserving certain subgroups of the center symmetry. For a gas of strings, the short time decay of the spectral form factor is governed by the continuous Hagedorn density of states, which can be associated to the thermal winding mode with winding number $\pm 1$. We show that the rise of the spectral form factor comes from other winding modes that also carry momentum along the time direction. We speculate on the existence of a family of classical solutions for these string modes, similar to the Horowitz-Polchinski solution. We review a similar problem for black holes. In particular, we examine the Kontsevich-Segal criterion on complex black holes that contribute to the spectral form factor. In the canonical ensemble quantity $Z(β+it)$, the black hole becomes unallowed at $t\sim \mathcal{O}(β)$. A way to avoid this is to consider the microcanonical ensemble, where the black hole stays allowable.
