Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics
Abstract
We present a theoretical framework for a class of generalized $U(1)$ gauge effective field theories. These theories are defined by specifying geometric patterns of charge configurations that can be created by local operators, which then lead to a class of generalized Gauss law constraints. The charge and magnetic excitations in these theories have restricted, subdimensional dynamics, providing a generalization of recently studied higher-rank symmetric $U(1)$ gauge theories to the case where arbitrary spatial rotational symmetries are broken. These theories can describe situations where charges exist at the corners of fractal operators, thus providing a continuum effective field theoretic description of Haah's code and Yoshida's Sierpinski prism model. We also present a $3+1$-dimensional $U(1)$ theory that does not have a non-trivial discrete $\mathbb{Z}_p$ counterpart.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.01855
- arXiv:
- arXiv:1806.01855
- Bibcode:
- 2018arXiv180601855B
- Keywords:
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- Condensed Matter - Strongly Correlated Electrons;
- High Energy Physics - Theory;
- Quantum Physics
- E-Print:
- 4+2 pages, 5 figures