发表机构
University of Cambridge（剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究BMN矩阵模型热力学，发现热分支在临界点$\mu/T=4\pi$处终结，一级相变不存在，相变与奇点重合，末端几何呈现普适颈部结构。
AI 中文摘要
我们在$N$大和强耦合下研究BMN矩阵模型的热力学，利用其在十一维超引力中的对偶黑洞。在一致截断到二维$SO(9)$规范超引力的框架内，静态$SO(3)\times SO(6)$不变黑洞满足常微分方程，我们对其进行了高精度求解。我们为该截断制定了全息重整化，并利用一个超对称解确定了有限反项。由此独立地给出能量、熵以及对BMN质量的响应，并沿该分支验证了第一定律和Smarr关系。热分支在$\mu/T$的临界值处终结，幂律拟合将其定位于$4\pi$，估计不确定度低于$10^{-10}$。早期工作中推断的一级相变（其中自由能由熵重构）不再成立，独立的十一维计算在我们覆盖的范围内与我们的结果一致。相反，自由能、熵和质量响应在分支末端连续地趋近于禁闭相中的值，此时解变为奇异的。如果该分支在其终点之前一直保持主导地位，那么相变因此与奇点重合。在分支末端附近，标量场遵循超对称一阶方程的解，而度规携带非平凡的blackening因子。视界发展出一个颈部，其轮廓是普适的，半径随距收缩点的距离的$2/5$次幂增长。在我们分辨的范围内，几何并非支配真空黑洞合并的Ricci平坦双锥。
英文摘要
We study the thermodynamics of the BMN matrix model at large $N$ and strong coupling, using its dual black holes in eleven-dimensional supergravity. Within the consistent truncation to two-dimensional $SO(9)$ gauged supergravity, the static $SO(3)\times SO(6)$-invariant black holes solve ordinary differential equations, which we solve to high precision. We formulate holographic renormalisation for this truncation and fix the finite counterterms using a supersymmetric solution. This gives the energy, the entropy and the response to the BMN mass independently, and we verify the first law and the Smarr relation along the branch. The thermal branch ends at a critical value of $μ/T$, which power-law fits place at $4π$ with an estimated uncertainty below $10^{-10}$. The first-order transition inferred in earlier work, where the free energy was reconstructed from the entropy, does not survive, and an independent eleven-dimensional calculation agrees with ours over the range it covers. Instead, the free energy, the entropy and the mass response approach their values in the confined phase continuously at the end of the branch, where the solutions become singular. If this branch remains the dominant one up to its end point, the transition therefore coincides with the singularity. Near the end of the branch, the scalar fields follow a solution of the supersymmetric first-order equations, while the metric carries a nontrivial blackening factor. The horizon develops a neck whose profile is universal, with radii growing as the $2/5$ power of the distance from the pinch. Within the range we resolve, the geometry is not that of the Ricci-flat double cone which governs mergers of vacuum black holes.
Comments45 pages, 5 figures. Comments welcome
