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

TL;DR

This paper investigates the relationship between exotic lattice models with subsystem symmetries and their continuum limits, revealing UV/IR mixing phenomena where long-distance physics depends on short-distance details.

Contribution

It provides a detailed analysis of the spectrum and correlation functions, uncovering subtleties in the continuum limit and demonstrating UV/IR mixing in these theories.

Findings

Continuum and infinite volume limits do not always commute.

UV/IR mixing indicates long-distance sensitivity to short-distance physics.

Spectrum analysis reveals subtleties in the continuum limit.

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.