Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

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.

More exotic field theories in 3+1 dimensions

“…In this paper, we continue the exploration in [3][4][5] of exotic continuum field theory in 3+1 dimensions and discuss new examples. As in [3][4][5], our theories are not Lorentz invariant. In fact, they are not even rotationally invariant.…”

“…As in [6], we will investigate these nonstandard quantum field theories by following their exotic global symmetries. Similar to the theories in [3][4][5], discontinuous field configurations play an important role in our analysis of the charged spectra under these global symmetries.…”

“…with a 2π-periodic θ -angle. This theory has no propagating degrees of freedom and is similar to the ordinary 1 + 1-dimensional U(1) gauge theory and to the 2 + 1-dimensional U(1) gauge theory of A in [4]. We compare these models in Table 2.…”

“…( Table 4: The four exotic U(1) global symmetries of [4] and their associated gauge fields. Each global symmetry is labeled by the S 4 representations (R time , R space ) for the temporal and spatial components of its conserved current.…”

“…In addition, our models also have parity and time reversal symmetries. Since many aspects of our discussion are similar to [3][4][5], we will be brief and we refer the reader to these papers for further details.…”