论文标题
TGFT中的相转换：环状势近似和等效到o $（n）$模型的功能重新归一化组
Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
论文作者
论文摘要
在量子重力的小组场理论方法中，预计连续的时空几何形状将通过相变出来。但是，了解重新归一化组流量下的相图并找到固定点仍然是一个主要挑战。在这项工作中，我们使用功能重归其化组方法解决了一个张力组域理论的问题。我们在任何限制到一个称为环状旋速的张力相互作用的子类的顺序下得出了有效电势的流程方程，并将投影到组空间中的恒定场。对于u $（1）$上的等级$ r $的张量字段，我们明确计算beta功能，并找到与o $（n）$型号的等效性，但有效的尺寸从$ r-1 $流向零。在$ R-1 $维度状态下，与O $（N）$模型的等效性通过张量的特定流量来修改异常尺寸的特定流，其结果是Wilson-Fisher型固定点解决方案具有两个分支。但是，由于流向零尺寸的流动，描述断裂相和不间断相之间的跃迁的固定点不会持续存在，我们发现通用的对称恢复。为了克服此限制，有必要超越紧凑的配置空间。
In the group field theory approach to quantum gravity, continuous spacetime geometry is expected to emerge via phase transition. However, understanding the phase diagram and finding fixed points under the renormalization group flow remains a major challenge. In this work we tackle the issue for a tensorial group field theory using the functional renormalization group method. We derive the flow equation for the effective potential at any order restricting to a subclass of tensorial interactions called cyclic melonic and projecting to a constant field in group space. For a tensor field of rank $r$ on U$(1)$ we explicitly calculate beta functions and find equivalence with those of O$(N)$ models but with an effective dimension flowing from $r-1$ to zero. In the $r-1$ dimensional regime, the equivalence to O$(N)$ models is modified by a tensor specific flow of the anomalous dimension with the consequence that the Wilson-Fisher type fixed point solution has two branches. However, due to the flow to dimension zero, fixed points describing a transition between a broken and unbroken phase do not persist and we find universal symmetry restoration. To overcome this limitation, it is necessary to go beyond compact configuration space.
