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ABJ anomaly as a U(1) symmetry and Noether's theorem
by Valentin Benedetti, Horacio Casini, Javier M. Magan
Submission summary
| Authors (as registered SciPost users): | Valentin Benedetti |
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| Preprint Link: | https://arxiv.org/abs/2309.03264v1 (pdf) |
| Date submitted: | 2024-02-21 15:14 |
| Submitted by: | Benedetti, Valentin |
| Submitted to: | SciPost Physics |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
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.