论文标题
在规范张量模型中的经典空间的出现
Emergence of classical spacetimes in canonical tensor model
论文作者
论文摘要
我们研究了Hamiltonian Monte Carlo方法在规范形式主义中的张量模型的波函数，用于谎言组对称或附近的波函数参数，并表明那里出现了Lie-Group对称对称的半古典空位。更确切地说，我们考虑了一些$（n+1）\（n = 1,2,3）$对称值的张量参数，并表明那里出现了离散的$ n $维度球。一个关键事实是，存在两个阶段，即经典阶段和量子阶段，具体取决于波函数的参数值，以及上面的经典空间的出现在前阶段发生，而在后一个阶段，配置的波动太大。这两个阶段之间的过渡与毛 - 宽大的跃迁或矩阵模型中的两切溶液之间的过渡相似。基于结果，我们对张量模型中的空间发展方式进行了一些猜测。
We study the wave function of a tensor model in the canonical formalism by Hamiltonian Monte Carlo method for Lie group symmetric or nearby values for the argument of the wave function, and show that there emerge Lie-group symmetric semi-classical spacetimes. More precisely, we consider some $SO(n+1)\ (n=1,2,3)$ symmetric values for the tensor argument of the wave function, and show that there emerge discrete $n$-dimensional spheres. A key fact is that there exist two phases, the classical phase and the quantum phase, depending on the values of the argument of the wave function, and emergence of classical spaces above occurs in the former phase, while fluctuations of configurations are too large for such emergence in the latter phase. The transition between the two phases has similarity with the Gross-Witten-Wadia transition, or that between the one-cut and the two-cut solutions in the matrix model. Based on the results, we give some speculations on how spacetimes evolve in the tensor model.
