论文标题
一维大N还原模型中的临界维度和负比热
Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models
论文作者
论文摘要
我们研究了YANG-MILLS（YM）型一维矩阵模型的关键现象，该模型是$ d+1 $ dimensional $ u（n）$ pure ym理论（Bosonic BFSS模型）的$ d+1 $ dimensional $ u（n）$ n $降低（或尺寸还原）。该模型显示了有限温度下的$ n $相变，这类似于原始YM理论的限制/解元过渡。我们通过“最低敏感性原理”以三循环计算来研究矩阵模型，并发现存在关键尺寸$ d = 35.5 $：在$ d \ le 35 $时，过渡是一阶的，而它是$ d \ ge ge 36 $的二阶订单。此外，我们在方法中评估了几个可观察物，它们很好地再现了现有的蒙特卡洛结果。通过仪表/重力对应关系，预计过渡与重力中的Gregory-laflamme转变有关，我们认为临界维度的存在与之一致。此外，在一阶过渡案例中，在微型典型合奏中出现了具有负比热的稳定相，这与Schwarzschild黑洞类似。我们研究此阶段的一些特性。
We investigate critical phenomena of the Yang-Mills (YM) type one-dimensional matrix model that is a large-$N$ reduction (or dimensional reduction) of the $D+1$ dimensional $U(N)$ pure YM theory (bosonic BFSS model). This model shows a large-$N$ phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory. We study the matrix model at a three-loop calculation via the "principle of minimum sensitivity" and find that there is a critical dimension $D=35.5$: At $D \le 35$, the transition is of first order, while it is of second order at $D\ge 36$. Furthermore, we evaluate several observables in our method, and they nicely reproduce the existing Monte Carlo results. Through the gauge/gravity correspondence, the transition is expected to be related to a Gregory-Laflamme transition in gravity, and we argue that the existence of the critical dimension is qualitatively consistent with it. Besides, in the first order transition case, a stable phase having negative specific heat appears in the microcanonical ensemble, which is similar to Schwarzschild black holes. We study some properties of this phase.
