论文标题
固定电荷扩展的分析结构
The analytic structure of the fixed charge expansion
论文作者
论文摘要
我们研究了不同时空维度中许多保形场理论的固定电荷扩展的分析性能。这里研究的模型是$ O（n）$和$ QED_3 $。我们表明，在$ d = 3-ε$尺寸中，以大型和消失的$ε$的双缩放限制获得的$ o（n）$固定电荷$ q $ q $保链维度是不可汇总的，doubly cotorial Divergent的，并且具有$ \ sqrt {q} $ optim tumpal truncation runcentress。通过使用复苏技术，我们表明，Borel平面中的奇异性与全球Instantons有关，这些偶数是在大型$ Q $和Ref的其他双级缩放限制中发现的。 [1]。在$ d = 4-ε$尺寸中，故事发生了变化，因为在同一大$ q $和小$ε$制度中，下一个订单校正对缩放维度的校正导致了收敛系列。重新召集的系列显示了一个新的分支切割奇点，这与负$ε$的$ o（n）$大电荷扇区的稳定性相关。尽管$ QED_3 $型号共享$ O（N）$型号的相同大量充电行为，但我们发现，在大量物质现场扩展中，大型电荷缩放尺寸是可borel的，单位段落的分歧，并且具有$ Q $ Q $最佳截断订单。
We investigate the analytic properties of the fixed charge expansion for a number of conformal field theories in different space-time dimensions. The models investigated here are $O(N)$ and $QED_3$. We show that in $d=3-ε$ dimensions the contribution to the $O(N)$ fixed charge $Q$ conformal dimensions obtained in the double scaling limit of large charge and vanishing $ε$ is non-Borel summable, doubly factorial divergent, and with order $\sqrt{Q}$ optimal truncation order. By using resurgence techniques we show that the singularities in the Borel plane are related to worldline instantons that were discovered in the other double scaling limit of large $Q$ and $N$ of Ref. [1]. In $d=4-ε$ dimensions the story changes since in the same large $Q$ and small $ε$ regime the next order corrections to the scaling dimensions lead to a convergent series. The resummed series displays a new branch cut singularity which is relevant for the stability of the $O(N)$ large charge sector for negative $ε$. Although the $QED_3$ model shares the same large charge behaviour of the $O(N)$ model, we discover that at leading order in the large number of matter field expansion the large charge scaling dimensions are Borel summable, single factorial divergent, and with order $Q$ optimal truncation order.
