论文标题
$ 1/n $的双向矢量模型
The bi-conical vector model at $1/N$
论文作者
论文摘要
我们研究了$ o（m）\ times o（n-m）$ vector模型的有限$ n $方面，具有四分之一的互动$ 2 \ leq d \ leq d \ leq 6 $ spacetime dimensions。最近已显示该模型显示出在$ d = 4-ε$ dimensions中的扰动Wilson-Fisher样固定点处的持续对称性破裂现象。双方模型的较大等级极限显示了真空的保形歧管和模量空间。我们找到了一组三个双重跟踪标量运算符，它们在一般$ d $中分别无关紧要，相关和边际变形。我们将单个和多跟踪标量算子的异常尺寸计算为大型等级扩展中的第一个子领先顺序。边际操作员的异常维度通常不会消失，这表明在有限的$ n $下取消了保形歧管。在同等排名的情况下，我们能够将各种运算符的缩放维度明确得出为仅$ d $的函数。
We study finite $N$ aspects of the $O(m)\times O(N-m)$ vector model with quartic interactions in general $2\leq d \leq 6$ spacetime dimensions. This model has recently been shown to display the phenomenon of persistent symmetry breaking at a perturbative Wilson-Fisher-like fixed point in $d=4-ε$ dimensions. The large rank limit of the bi-conical model displays a conformal manifold and a moduli space of vacua. We find a set of three double trace scalar operators that are respectively irrelevant, relevant and marginal deformations of the conformal manifold in general $d$. We calculate the anomalous dimensions of the single and multi-trace scalar operators to the first sub-leading order in the large rank expansion. The anomalous dimension of the marginal operator does not vanish in general, indicating that the conformal manifold is lifted at finite $N$. In the case of equal ranks we are able to derive explicitly the scaling dimensions of various operators as functions of only $d$.
