格点上的全息学：来自三维超对称杨-米尔斯理论的证据
Holography on the lattice: Evidence from 3D supersymmetric Yang--Mills theory
AI总结：
研究三维超对称杨-米尔斯理论的非微扰相图，通过格点方法保持部分超对称代数，探讨空间脱困相变与全息对应关系，验证高温大N预测的相变温度比例关系。
摘要：
我们通过格点研究最大超对称杨-米尔斯理论，聚焦其非微扰相图。使用在有限格点间距下保持部分超对称代数的格点形式，研究空间脱困相变，全息学将其与双极引力理论中局部与均匀黑洞膜的相变联系起来。分析采用$N_L^2 \times N_T$格点，$N=8$颜色在SU($N$)规范群中，考虑$N_T=8$、10和12，每种情况的长宽比$α= N_L/N_T \leq 3$。得到的相变温度与全息低温度、大N预测$T_c \propto α^3$一致，进一步证明该设定下的规范-引力对应关系。
英文摘要：
We present new results from our lattice investigations of maximally supersymmetric Yang--Mills theory in three dimensions, focusing on its nonperturbative phase diagram. Using a lattice formulation that preserves part of the supersymmetry algebra at finite lattice spacing, we study the spatial deconfinement transition, which holography relates to the transition between localized and homogeneous black branes in the dual gravity theory. Our analysis employs $N_L^2 \times N_T$ lattices with $N = 8$ colors in the SU($N$) gauge group, considering $N_T = 8$, $10$ and $12$, in each case with aspect ratios $α= N_L/N_T \leq 3$. The resulting transition temperatures are consistent with the holographic low-temperature, large-$N$ prediction $T_c \propto α^3$, providing further evidence for the gauge--gravity correspondence in this setting.
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