We extend the recent one-loop analysis of the ultraviolet completion of the [Formula: see text] nonlinear [Formula: see text] model in six dimensions to two-loop order in the [Formula: see text] scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and [Formula: see text]-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 nontrivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson–Fisher fixed point are consistent with the [Formula: see text] expansion of the respective large [Formula: see text] exponents of the underlying universal theory. Using the Ward–Takahashi identity we deduce the three-loop [Formula: see text] renormalization group functions for the six-dimensional ultraviolet completeness of scalar QED.

中文翻译：

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ℂℙ(N) σ 模型在两个循环处的六维紫外完成

我们将最近对 [公式：见文本] 非线性 [公式：见文本] 模型的六维紫外完成单环分析扩展到任意协变规范的 [公式：见文本] 方案中的二环阶. 特别是，我们计算了四个耦合常数的场和[公式：见文本]-函数的异常维度。我们注意到，与四个维度的量子电动力学（QED）一样，物质场异常维度仅取决于一个循环的规范参数。作为一项重要的检查，我们验证在 Wilson-Fisher 不动点从这些重整化群函数导出的临界指数与基础普遍理论的相应大 [公式：见文本] 指数的 [公式：见文本] 展开一致.