Abstract
We extend our exploration of nonstandard continuum quantum field theories in 2+12+1 dimensions to 3+13+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global U(1)U(1) symmetry and in a followup paper we will study models with a global \mathbb{Z}_NℤN symmetry.
Highlights
We extend our exploration of nonstandard continuum quantum field theories in 2 + 1 dimensions to 3 + 1 dimensions
In every one of these dual pairs the global symmetries and the spectra match across the duality. (See Table 3 and Table 4.) This is surprising given the subtle nature of the states that are charged under the momentum and winding symmetries of the non-gauge systems and the subtle nature of the states that are charged under the magnetic and the electric symmetries of the gauge systems
Consider a 3 + 1-dimensional quantum field theory with an ordinary U(1) global symmetry that is associated with a Noether current Jμ
Summary
Common lore states that the low-energy behavior of every lattice system can be described by a continuum quantum field theory. (See Table 3 and Table 4.) This is surprising given the subtle nature of the states that are charged under the momentum and winding symmetries of the non-gauge systems and the subtle nature of the states that are charged under the magnetic and the electric symmetries of the gauge systems These two dual pairs of theories, A/φand A/φ, will be the building blocks of the N tensor gauge theory in [4], which is the continuum field theory for the X-cube model [34]. Consider a 3 + 1-dimensional quantum field theory with an ordinary U(1) global symmetry that is associated with a Noether current Jμ. Consider a continuum field theory with operators (J0I , J K ) where the index I and K are respectively in representation R time and R space of the spatial rotation group. We have 2L x + 2L y + 2Lz − 3 such charges
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