论文标题
$ cp（n）$σ$模型的六维紫外线完成
Six dimensional ultraviolet completion of the $CP(N)$ $σ$ model at two loops
论文作者
论文摘要
我们对六个维度的$ cp（n）$ nlinear $σ$模型的紫外线完成的最新环路分析扩展到了MSBAR方案中的两个环订单，以进行任意协变量量表。特别是，我们计算了四个耦合常数的磁场的异常尺寸和$β$ - 功能。我们注意到，就像四个维度中的量子电动力学（QED）一样，物质场异常的维度仅取决于一个循环的量规参数。作为一项非平凡检查，我们验证了Wilson-Fisher固定点的这些重新归化组功能所获得的关键指数与基础通用理论的各个大型$ N $指数的$ε$扩展是一致的。使用病房 - 塔卡哈西身份，我们推断出六维紫外线QED的六维紫外线完整性的三个环MSBAR重新归一化组函数。
We extend the recent one loop analysis of the ultraviolet completion of the $CP(N)$ nonlinear $σ$ model in six dimensions to two loop order in the MSbar scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and $β$-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a non-trivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson-Fisher fixed point are consistent with the $ε$ expansion of the respective large $N$ exponents of the underlying universal theory. Using the Ward-Takahashi identity we deduce the three loop MSbar renormalization group functions for the six dimensional ultraviolet completeness of scalar QED.
