## Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

Nathan Seiberg, Shu-Heng Shao

SciPost Phys. 10, 003 (2021) · published 8 January 2021

### Abstract

Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the low-energy physics of the X-cube model. A key aspect of our constructions is the use of discontinuous fields in the continuum field theory. Spacetime is continuous, but the fields are not.

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