Abstract
We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.
Highlights
We discuss nonstandard continuum quantum field theories in 2 + 1 dimensions
If the global symmetry group is compact such as U(1) or N, this means that the charge operator can be discontinuous as a function of the position
We will encounter situations where it is meaningful to study them in the continuum limit. This happens because these states are the lowest energy states that are charged under some global symmetry
Summary
This paper is the first in a sequence of three papers (the other papers are [1, 2]). Here we will study systems in 2 + 1 dimensions and in [1, 2] we will consider similar systems in 3 + 1 dimensions. (A followup paper [3] explores additional models.) The goal of these papers is to present a continuum quantum field theory perspective of some lattice models studied in the condensed matter literature, and in particular of models of fractons. The gapped fracton models have a ground state degeneracy proportional to the length of the system.1 Is such behavior surprising from a continuum quantum field theory point of view, it is infinite in the continuum limit. If the global symmetry group is compact such as U(1) or N , this means that the charge operator can be discontinuous as a function of the position These three characteristics seem impossible in the context of continuum quantum field theory. A continuum quantum field theory gives us a universal description of the low-energy physics, which does not depend on most of the details of the microscopic model. We will encounter situations where it is meaningful to study them in the continuum limit This happens because these states are the lowest energy states that are charged under some global symmetry.
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