Anomalous continuous translations
Nathan Seiberg
SciPost Phys. 19, 031 (2025) · published 11 August 2025
Part of the In Memoriam: Ian Affleck Collection in the In Memoriam Series.
- doi: 10.21468/SciPostPhys.19.2.031
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Abstract
We discuss a large class of non-relativistic continuum field theories where the Euclidean spatial symmetry of the classical theory is violated in the quantum theory by an Adler-Bell-Jackiw-like anomaly. In particular, the continuous translation symmetry of the classical theory is broken in the quantum theory to a discrete symmetry. Furthermore, that discrete symmetry is extended by an internal symmetry, making it non-Abelian. This presentation streamlines and extends the discussion in [SciPost Phys. 18, 063 (2025)]. In an Appendix, we present an elementary introduction to 't Hooft and Adler-Bell-Jackiw anomalies using a well-known system.
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