论文标题
$ d = 6 $ dimensions的$ ϕ^3 $理论的重新归一化组行为
Renormalization-Group Behavior of $ϕ^3$ Theories in $d=6$ Dimensions
论文作者
论文摘要
我们使用计算为四环级别的beta函数，在$ ϕ^3 $中以$ ϕ^3 $理论为$ ϕ^3 $理论的非零耦合处的可能的重归化组固定点。我们分析了这种类型的三种理论，其中（a）一个单一组件标量，（b）变换为全局$ {\ rm su}（n）$对称组的基本表示，以及（c）作为全局$ $ {\ rm su}（\ rm su}（n）$的标量变换为Bi-Adjoint的代表。我们找不到关于理论（a）或（b）中此类固定点的可靠证据。理论（C）具有特殊特征，即Beta函数中的单循环项为零。讨论了这一点的含义。
We investigate possible renormalization-group fixed points at nonzero coupling in $ϕ^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a one-component scalar, (b) a scalar transforming as the fundamental representation of a global ${\rm SU}(N)$ symmetry group, and (c) a scalar transforming as a bi-adjoint representation of a global ${\rm SU}(N) \otimes {\rm SU}(N)$ symmetry. We do not find robust evidence for such fixed points in theories (a) or (b). Theory (c) has the special feature that the one-loop term in the beta function is zero; implications of this are discussed.
