论文标题
3D张量 - 马trix模型的CDT开放闭合表面场理论
CDT open-closed surface field theory of a 3D tensor-matrix model
论文作者
论文摘要
我们构建了一个张量 - 矩阵模型，该模型描述了开放闭合表面的3维（3D）因果动力学三角剖分（CDT）。尽管表面的通常分裂相互作用不是从随机量化过程中得出的，但它提供了IK型的另一种相互作用，这成为唯一的量子校正。通过双缩放限制，它实现了CDT开放闭合的表面场理论，包括在相同条件下与封闭的表面CDT模型的IK型相互作用。此外，在Fokker-Planck（FP）Hamiltonian中，我们研究了发电机的换向关系，对于边界回路数量最低的表面。在我们的3D模型中，发电机似乎与2D模型不同，在我们的3D模型中，当换向器包含开放字符串边缘的发生器时，代数结构并不精确。
We construct a tensor-matrix model which describes 3-dimensional (3D) Causal Dynamical Triangulation (CDT) of open-closed surface. Though the usual splitting interaction of a surface is not derived from the stochastic quantization procedure, it provides another interaction of IK-type, which becomes the sole quantum correction. Through the double scaling limit, it realizes CDT open-closed surface field theory including the IK-type interactions in the same condition with the closed surface CDT model. Further, we investigate the commutation relations of the generators, for surfaces with the lowest numbers of boundary loops, in the Fokker-Planck (FP) Hamiltonian. The generators seem to close in their commutation relations in our 3D model, differently from the 2D model, where the algebraic structure was not exact when commutators contain the generator of the open string edge.
