Emergence of Lie group symmetric classical spacetimes in the canonical tensor model
Emergence of Lie group symmetric classical spacetimes in the canonical tensor model
复制标题
正则张量模型中李群对称经典时空的出现
DOI：
10.1093/ptep/ptac045
复制
发表时间：
2022
影响因子：
3.5
通讯作者：
Sasakura Naoki
中科院分区：
文献类型：
--
作者：
Kawano Taigen;Sasakura Naoki
本文在正则形式下分析了张量模型的波函数，当波函数的参数取李群不变值或附近值时。数值计算表明，它有两个相，我们称之为量子相和经典相。在经典条件下，相位涨落被抑制，出现了李群对称条件下经典几何空间不变的离散化构型。通过检查出现构型的拓扑和几何（拉普拉斯）性质，明确地证明了sn （n= 1,2,3）对于so （n+ 1）对称的出现。这两个阶段之间的转换具有变量分布的分裂/合并的形式，类似于矩阵模型的对应物，即在单切解和双切解之间的转换。然而，这种相似性被我们设置中的分布机制与矩阵模型中的分布机制的差异所掩盖。我们还将这种转变作为复制对称性破缺来讨论。我们对这些参数值的相的性质和过渡进行了各种初步的研究。
We analyze a wave function of a tensor model in the canonical formalism, when the argument of the wave function takes Lie group invariant or nearby values. Numerical computations show that there are two phases, which we call the quantum and the classical phases. In the classical phase fluctuations are suppressed, and configurations emerge which are discretizations of classical geometric spaces invariant under Lie group symmetries. This is explicitly demonstrated for emergence ofSn(n= 1, 2, 3) forSO(n+ 1) symmetries by checking the topological and geometric (Laplacian) properties of the emerging configurations. The transition between the two phases has the form of splitting/merging of distributions of variables, resembling a matrix model counterpart, namely the transition between one-cut and two-cut solutions. However, this resemblance is obscured by a difference in the mechanism of distribution in our setup from that in the matrix model. We also discuss this transition as a replica symmetry breaking. We perform various preliminary studies of the properties of the phases and the transition for such values of the argument.