一维大N约化模型的临界维数与负Specific Heat
Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models
摘要：
研究了Yang-Mills（YM）型一维矩阵模型的临界现象，该模型是$D+1$维$U(N)$纯YM理论（玻色子BFSS模型）的大$N$约化（或降维）.该模型显示了一个大的- $N$相变在有限的温度下，这是类似于原来的YM理论的限制/解除限制的转变。我们用“最小灵敏度原理”研究了矩阵模型的三圈计算，发现存在一个临界维数$D=35.5$：在$D \le 35$，跃迁为一阶，而在$D\ge 36$，跃迁为二阶.此外，我们在我们的方法中评估几个可观的，他们很好地再现现有的蒙特卡罗结果。通过规范/引力对应，我们认为该跃迁与引力中的Gregory-Laflamme跃迁有关，并且临界维数的存在与之定性一致，此外，在一阶跃迁情形下，微正则系综中出现了一个具有负比热的稳定相，类似于Schwarzschild黑洞.我们研究了这一阶段的一些性质。
英文摘要：
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.
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