论文标题
在$ \ varepsilon $扩展中，在多个耦合标量理论中对固定点的重型寻求固定点
Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\varepsilon$ Expansion
论文作者
论文摘要
在$ \ varepsilon $中以$ 4- \ varepsilon $和$ 3- \ varepsilon $ dimensions的$ \ varepsilon $扩展中的非微不足道完全相互作用的固定点的张力方程，用于$ n $ n $ components和相应的多个Index couplings $λ$ cupplings $λ$ symetric symetric syt sytorric tosors sysors sysors sysors sysors sysors sysors sysors $ n $ components $ dimensions。使用分析方法和数值方法。对于$ n = 5,6,7 $，在四个索引案例中，在数值上发现了大量的非理性固定点，其中$ ||λ||^2 $接近Rychkov和Arxiv中的rychkov和Stergiou的界限：1810.10541。除了已经已知的那些外，没有其他解决方案饱和。通常，这些示例在该领域没有独特的二次不变。对于$ n \ geqslant 6 $，在整个耦合空间中的稳定矩阵总是具有负特征值。在六个索引情况下，数值搜索为$ n = 5 $生成了大量的解决方案。
The tensorial equations for non trivial fully interacting fixed points at lowest order in the $\varepsilon$ expansion in $4-\varepsilon$ and $3-\varepsilon$ dimensions are analysed for $N$-component fields and corresponding multi-index couplings $λ$ which are symmetric tensors with four or six indices. Both analytic and numerical methods are used. For $N=5,6,7$ in the four-index case large numbers of irrational fixed points are found numerically where $||λ||^2$ is close to the bound found by Rychkov and Stergiou in arXiv:1810.10541. No solutions, other than those already known, are found which saturate the bound. These examples in general do not have unique quadratic invariants in the fields. For $N \geqslant 6$ the stability matrix in the full space of couplings always has negative eigenvalues. In the six index case the numerical search generates a very large number of solutions for $N=5$.
