论文标题
BMN矩阵模型的新几何形状
Emergent Geometries from the BMN Matrix Model
论文作者
论文摘要
我们回顾了BMN矩阵模型中出现几何形状的最新结果，BMN矩阵模型是一种一维理论，被认为是平面波几何形状上M理论的非扰动公式。了解新兴几何形状的关键是BPS操作员的特征值分布。规方法计算表明，BPS操作员在仪表/重力二元性中重现了相应的超级溶液，以及M-Brane图片中的Brane几何形状。在有限的温度下，应以非平凡的方式实现这些几何形状。蒙特卡洛对该轨迹理论的模拟揭示了两种相变的类型：限制/反登录过渡和迈尔斯的过渡，这些过渡提供了对几何形状出现的见解。尤其是，数值结果在定性上与重力侧预测的限制/解密过渡的临界温度一致。
We review recent results of emergent geometries in the BMN matrix model, a one-dimensional gauge theory considered as a non-perturbative formulation of M-theory on the plane-wave geometry. A key to understand the emergent geometries is the eigenvalue distribution of a BPS operator. Gauge-theory calculation shows that the BPS operator reproduces the corresponding supergravity solutions in the gauge/gravity duality and also brane geometries in the M-brane picture. At finite temperatures, these geometries should be realised in a non-trivial way. Monte Carlo simulations of this gauge theory revealed two types of phase transitions: the confinement/deconfinement transition and the Myers transition, which provide insights into the emergence of the geometries. Especially, the numerical results qualitatively agree with the critical temperature of the confinement/deconfinement transition predicted on the gravity side.
