论文标题
$ o（n）$对称模型中$ ϕ^q $运算符的六环异常维度
Six-loop anomalous dimension of the $ϕ^Q$ operator in the $O(N)$ symmetric model
论文作者
论文摘要
一项大电荷扩展技术为计算运营商的关键维度$ ϕ^q $的关键维度提供了新的机会。在小耦合方案中，可以从固定$ Q $的许多直接扰动计算中固定异常尺寸的多项式结构。在六环级别上，需要包括与五个或更多腿的操作员相对应的新图。后者从未出现在标量理论计算中。在这里，我们展示了如何按六循环订单计算运算符$ ϕ^{q = 5} $的异常尺寸。结合$ Q <5 $的运营商的结果，这些结果是从六环β函数中提取的通用标量理论，以及从大电荷扩展中的预测，我们的计算使我们能够为总体上的答案得出答案。在临界点重新召集三个维度，使我们能够将关键指数与蒙特卡洛模拟的结果和大型预测进行比较。
A technique of large-charge expansion provides a novel opportunity for calculation of critical dimensions of operators $ϕ^Q$ with fixed charge $Q$. In the small-coupling regime the polynomial structure of the anomalous dimensions can be fixed from a number of direct perturbative calculations for a fixed $Q$. At the six-loop level one needs to include new diagrams that correspond to operators with five or more legs. The latter never appeared before in scalar-theory calculations. Here we show how to compute the anomalous dimension of the operator $ϕ^{Q=5}$ at the six-loop order. In combination with results for operators with $Q<5$, which are extracted from the six-loop beta-functions for general scalar theory, and with predictions from the large-charge expansion, our calculation allows us to derive the answer for general-$Q$ anomalous dimensions. At the critical point resummation in three dimensions enables us to compare the critical exponents with results of Monte-Carlo simulations and large-$N$ predictions.
