理论空间中的局部性
Locality in Theory Space
摘要：
定域性是构造现实量子场论的指导原则。紧化理论提供了一个有趣的背景来考虑局部性，因为相互作用在紧方向上可以是非局部的，而在扩展方向上仍然是局部的。本文研究了五维杨-米尔斯的维数解构四维拉格朗日量在“理论空间”中的定域性。在显式紫外线（UV）完备化中，人们可以通过非局部算子的不相关性来理解理论空间局部性的起源。然而，从红外（IR）的角度来看，理论空间局域性似乎并不是一个特殊的属性，因为最低层的卡鲁扎-克莱因（KK）模式只是由规范的非线性西格玛模型描述，局域性对KK光谱和相互作用施加了看似任意的约束。我们认为，这些限制是重要的，但从IR的角度来看，因为它们影响了四维截断的理论，高能量散射击中强耦合。有趣的是，我们发现，最大限度地提高这个截止尺度意味着五维局域性。以这种方式，理论空间局部性与IR中的弱耦合相关，独立于UV考虑。我们简要地评论其他方案，最大限度地提高截止尺度产生有趣的物理，包括理论空间描述QCD和反德西特空间的解构。
英文摘要：
Locality is a guiding principle for constructing realistic quantum field theories. Compactified theories offer an interesting context in which to think about locality, since interactions can be nonlocal in the compact directions while still being local in the extended ones. In this paper, we study locality in "theory space", four-dimensional Lagrangians which are dimensional deconstructions of five-dimensional Yang-Mills. In explicit ultraviolet (UV) completions, one can understand the origin of theory space locality by the irrelevance of nonlocal operators. From an infrared (IR) point of view, though, theory space locality does not appear to be a special property, since the lowest-lying Kaluza-Klein (KK) modes are simply described by a gauged nonlinear sigma model, and locality imposes seemingly arbitrary constraints on the KK spectrum and interactions. We argue that these constraints are nevertheless important from an IR perspective, since they affect the four-dimensional cutoff of the theory where high energy scattering hits strong coupling. Intriguingly, we find that maximizing this cutoff scale implies five-dimensional locality. In this way, theory space locality is correlated with weak coupling in the IR, independent of UV considerations. We briefly comment on other scenarios where maximizing the cutoff scale yields interesting physics, including theory space descriptions of QCD and deconstructions of anti-de Sitter space.
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