The low-energy limit of some exotic lattice theories and UV/IR mixing

TL;DR

This work analyzes exotic lattice theories with subsystem global symmetries, focusing on the 2+1d XY-plaquette model and its modified Villain formulation to illuminate their relation to a continuum $\phi$-theory. By examining spectra and a broad set of correlation functions, the authors reveal UV/IR mixing and noncommuting continuum and infinite-volume limits, while establishing a self-dual, anomaly-rich continuum framework that captures the light plane-wave sector and treats charged operators as defects or redundant in the IR. They show that small deformations preserve the gapless phase and anomaly structure, whereas larger deformations can drive the system toward conventional 2+1d bosonic theories, with precise anomaly matching guiding the IR fate. The analysis extends to 3+1d theories, exposing similar limit-order sensitivities and dualities between $\phi$-type theories and tensor-gauge duals, thereby offering a unified picture of how exotic lattice constructions map to robust continuum descriptions and how UV detail influences IR physics.

Abstract

We continue our exploration of exotic, gapless lattice and continuum field theories with subsystem global symmetries. In an earlier paper, we presented free lattice models enjoying all the global symmetries (except continuous translations), dualities, and anomalies of the continuum theories. Here, we study in detail the relation between the lattice models and the corresponding continuum theories. We do that by analyzing the spectrum of the theories and several correlation functions. These lead us to uncover interesting subtleties in the way the continuum limit can be taken. In particular, in some cases, the infinite volume limit and the continuum limit do not commute. This signals a surprising UV/IR mixing, i.e., long distance sensitivity to short distance details.