通过跨系列实现非威尔逊紫外完备化
Non-Wilsonian ultraviolet completion via transseries
摘要：
我们研究了一些微扰重整化程序的影响时，增加了Borel-Ecalle重定。我们证明了标量$ϕ^4$模型的一种新的非微扰不动点的出现，它代表了一个紫外自完成的transseries。我们认为，这种完成是纯粹的非威尔逊，它取决于一个任意常数源于transseries解决方案的重整化群方程。另一方面，如果通过调整这个任意常数不需要固定点，我们最终得到一个有效的理论，其中标量质量对截止值是二次敏感的，即使在维度正则化中也有效。标量质量与能量尺度的完全解耦可以用来确定非渐近自由模型中重正子的Borel-Laplace重正化的物理处方。我们还评论可能的正交方案，在文献中可能发挥作用时，不存在固定点。
英文摘要：
We study some of the implications for the perturbative renormalization program when augmented with the Borel-Ecalle resummation. We show the emergence of a new kind of non-perturbative fixed point for the scalar $ϕ^4$ model, representing an ultraviolet self-completion by transseries. We argue that this completion is purely non-Wilsonian and it depends on one arbitrary constant stemming from the transseries solution of the renormalization group equation. On the other hand, if no fixed points are demanded through the adjustment of this arbitrary constant, we end up with an effective theory in which the scalar mass is quadratically-sensitive to the cut-off, even working in dimensional regularization. Complete decoupling of the scalar mass to this energy scale can be used to determine a physical prescription for the Borel-Laplace resummation of the renormalons in non-asymptotically free models. We also comment on possible orthogonal scenarios available in the literature that might play a role when no fixed points exist.
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