# Locality in theory space

## Abstract

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.