标题： 时空几何流形中的相变：因果完备的洛伦兹巴雷特-克兰模型的朗道-金兹堡分析 显示英文标题

标题： Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model

摘要： 预期在张量群场理论（TGFT）方法中，连续时空会通过相变出现。最近对将朗道-金兹堡平均场理论应用于越来越现实的TGFT模型的研究已经展示了如何在其中实现相变。在这里，我们进一步发展了这一设定，并考虑了因果完整的洛伦兹巴雷特-克兰（BC）模型，该模型不仅包括类空四面体，还包括类时和类光四面体作为量子几何构建块。此外，我们通过群场的$\mathbb{R}$-值变量引入离散标量场。在此背景下，我们分析了具有任意单个单纯形和张量不变类型的相互作用的模型，将其扩展到从因果动态三角化中广为人知的两个顶点模型，并还考虑了一个具有颜色单纯形相互作用的模型。作为主要结果，我们证明对于所有这些情况，都可以实现向非平凡凝聚态的相变的平均场近似。特别是，我们表明临界行为完全由由洛伦兹群的提升部分所表征的类空面驱动。后者导致涨落的指数抑制，从而稳定平均场真空。相反，类时面在此不起作用，因为它们由洛伦兹群的旋转部分，即紧致部分所表征。由于这种状态通常被大量的TGFT量子填充，我们的工作进一步有力地支持了因果完整的TGFT模型存在合理的连续引力区域。我们的结果也间接加强了有效宇宙动力学的推导以及最近在平均场近似下对标量宇宙扰动的研究。 显示英文摘要

摘要： It is expected that continuum spacetime emerges via phase transition in the tensorial group field theory (TGFT) approach to quantum gravity. Recent work on the application of Landau-Ginzburg mean-field theory to progressively realistic TGFT models has demonstrated how phase transitions can be realized therein. Here, we further develop this setting and consider the causally complete Lorentzian Barrett-Crane (BC) model which includes not only spacelike but also timelike and lightlike tetrahedra as quantum geometric building blocks. In addition, we incorporate discretized scalar fields by $\mathbb{R}$-valued variables of the group fields. In this context, we analyze models with an arbitrary single interaction of simplicial and tensor-invariant type, extend it to the model with the two vertices well-known from causal dynamical triangulations, and also consider a model with colored simplicial interactions. As a main result, we demonstrate for all those cases that a mean-field approximation of a phase transition towards a non-trivial condensate state can always be realized. In particular, we show that the critical behavior is entirely driven by spacelike faces which are characterized by the boost part of the Lorentz group. The latter induces an exponential suppression of fluctuations which then stabilizes the mean-field vacuum. In contrast, timelike faces do not play a role in this as they are characterized by the rotational and thus compact part of the Lorentz group. Since such a state is typically populated by a large number of TGFT quanta, our work lends further considerable support to the existence of a sensible continuum gravitational regime for causally complete TGFT models. Our results also indirectly strengthen the derivation of effective cosmological dynamics and the recently improved study of scalar cosmological perturbations within a mean-field approximation.