论文标题
来自旋速树的张量模型中的非扰动缺陷
Non-Perturbative Defects in Tensor Models from Melonic Trees
论文作者
论文摘要
Klebanov-Tarnopolsky张量模型是一种具有某些四分之一潜能的级别三张量标量场的量子场理论。该理论具有不寻常的大$ n $限制,称为旋速限制,该极限是强烈耦合但可解决的,在大距离上产生了一个罕见的非扰动非抑制性非对比的综合场理论,该理论可以接受分析解决方案。我们研究了张量模型中缺陷的动力学,该模型由$ p $维二维子空间中的局部磁场耦合定义。虽然我们与一般$ p $和$ d $一起工作,但物理上有趣的病例包括$ d = 2,3 $的线缺陷和$ d = 3 $的表面缺陷。通过确定在存在缺陷的情况下概括旋速限制的新型大$ n $限制,我们证明标量场的缺陷单点函数仅从梅洛克树形状的Feynman图的子集中获得贡献。这些图可以使用封闭的Schwinger-Dyson方程来重新亮相,这使我们能够非扰动地确定此缺陷单点函数。在较大距离的情况下,我们发现的解决方案描述了非平凡的保形缺陷,我们讨论了它们的缺陷重新归一化组(RG)流。特别是,对于线路缺陷,我们解决了$ d = 4-ε$之间的琐碎和保形线之间的精确RG流。我们还计算确切的线路缺陷熵并验证$ g $ - 理论。此外,我们通过操作员实行扩展分析了标量场的缺陷两点函数及其分解,为双线性操作员和应力能量张量提供明确的公式。
The Klebanov-Tarnopolsky tensor model is a quantum field theory for rank-three tensor scalar fields with certain quartic potential. The theory possesses an unusual large $N$ limit known as the melonic limit that is strongly coupled yet solvable, producing at large distance a rare example of non-perturbative non-supersymmetric conformal field theory that admits analytic solutions. We study the dynamics of defects in the tensor model defined by localized magnetic field couplings on a $p$-dimensional subspace in the $d$-dimensional spacetime. While we work with general $p$ and $d$, the physically interesting cases include line defects in $d=2,3$ and surface defects in $d=3$. By identifying a novel large $N$ limit that generalizes the melonic limit in the presence of defects, we prove that the defect one-point function of the scalar field only receives contributions from a subset of the Feynman diagrams in the shape of melonic trees. These diagrams can be resummed using a closed Schwinger-Dyson equation which enables us to determine non-perturbatively this defect one-point function. At large distance, the solutions we find describe nontrivial conformal defects and we discuss their defect renormalization group (RG) flows. In particular, for line defects, we solve the exact RG flow between the trivial and the conformal lines in $d=4-ε$. We also compute the exact line defect entropy and verify the $g$-theorem. Furthermore we analyze the defect two-point function of the scalar field and its decomposition via the operator-product-expansion, providing explicit formulae for one-point functions of bilinear operators and the stress-energy tensor.