论文标题
张量现场理论和旋速固定点的重新归一化
Renormalization in tensor field theory and the melonic fixed point
论文作者
论文摘要
本论文的重点是张量场理论的重新归一化。它的第一部分认为具有$ O（n）^3 $对称性和远程传播器的四分之一张量模型。建立了任何$ n $的任何$ d $中的非扰动固定点的存在。我们发现了由所谓的四面体耦合参数参数化的四行固定点。其中之一是红外的吸引力，互动的，并引起了一种新型的CFT，称为Melonic CFTS，然后进行更多细节进行研究。我们首先在固定点计算双线性和OPE系数的尺寸，这些尺寸与$ n $的单一CFT一致。然后，我们计算$ 1/n $更正。在临近领先的顺序下，固定点的线倒入一个固定点。但是，校正是复杂的，在NLO时单位性损坏。最后，我们表明该模型尊重$ f $ - 理论。论文的下一部分调查了六张张量田野理论的排名$ 3 $和5美元。在等级$ 3 $中，我们发现了两个IR稳定的实际固定点，在短范围内，一条IR稳定的真实固定点在远距离范围内。令人惊讶的是，排名$ 5 $的唯一固定点是高斯。对于排名$ 3 $的型号，在短期情况下，我们仍然在NLO找到两个IR稳定固定点。但是，在远程情况下，对固定点的校正是非扰动的，因此不可靠：我们没有发现大$ N $固定点的前体。论文的最后一部分调查了表现出旋律大$ n $限制的模型类。我们证明，具有张量的型号以$ O（n）$ o（n）$或$ sp（n）$ 5 $ 5 $的不可约表示，确实承认了$ n $的限制。这种概括依赖于从涉及模型扰动扩展的Feynman图的详细组合分析中得出的递归界限。
This thesis focuses on renormalization of tensor field theories. Its first part considers a quartic tensor model with $O(N)^3$ symmetry and long-range propagator. The existence of a non-perturbative fixed point in any $d$ at large $N$ is established. We found four lines of fixed points parametrized by the so-called tetrahedral coupling. One of them is infrared attractive, strongly interacting and gives rise to a new kind of CFT, called melonic CFTs which are then studied in more details. We first compute dimensions of bilinears and OPE coefficients at the fixed point which are consistent with a unitary CFT at large $N$. We then compute $1/N$ corrections. At next-to-leading order, the line of fixed points collapses to one fixed point. However, the corrections are complex and unitarity is broken at NLO. Finally, we show that this model respects the $F$-theorem. The next part of the thesis investigates sextic tensor field theories in rank $3$ and $5$. In rank $3$, we found two IR stable real fixed points in short range and a line of IR stable real fixed points in long range. Surprisingly, the only fixed point in rank $5$ is the Gaussian one. For the rank $3$ model, in the short-range case, we still find two IR stable fixed points at NLO. However, in the long-range case, the corrections to the fixed points are non-perturbative and hence unreliable: we found no precursor of the large $N$ fixed point. The last part of the thesis investigates the class of model exhibiting a melonic large $N$ limit. We prove that models with tensors in an irreducible representation of $O(N)$ or $Sp(N)$ in rank $5$ indeed admit a large $N$ limit. This generalization relies on recursive bounds derived from a detailed combinatorial analysis of Feynman graphs involved in the perturbative expansion of our model.
