ABJ anomaly as a U(1) symmetry and Noether's theorem
Sep 6, 2023
Published in:
- SciPost Phys. 18 (2025) 041
e-Print:
- 2309.03264 [hep-th]
DOI:
- 10.21468/SciPostPhys.18.2.041 (publication)
View in:
Citations per year
Abstract: (arXiv)
The Adler-Bell-Jackiw anomaly determines the violation of chiral symmetry when massless fermions are coupled to an abelian gauge field. In its seminal paper, Adler noticed that a modified chiral U(1) symmetry could still be defined, at the expense of being generated by a non-gauge-invariant conserved current. We show this internal U(1) symmetry has the special feature that it transforms the Haag duality violating sectors (or non-local operator classes). This provides a simple unifying perspective on the origin of anomaly quantization, anomaly matching, applicability of Goldstone theorem, and the absence of a Noether current. We comment on recent literature where this symmetry is considered to be either absent or non-invertible. We end by recalling the DHR reconstruction theorem, which states 0-form symmetries cannot be non-invertible for d>2, and argue for a higher-form symmetry reconstruction theorem.Note:
- To appear in SciPost Physics
- symmetry: U(1)
- operator: nonlocal
- fermion: massless
- duality: violation
- symmetry: chiral
- current: Noether
- current: conservation law
- gauge field theory: abelian
- anomaly
- Goldstone theorem
References(71)
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