ABJ anomaly as a U(1) symmetry and Noether's theorem
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| Format: | Preprint |
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2023
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| _version_ | 1866916596054753280 |
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| author | Benedetti, Valentin Casini, Horacio Magan, Javier M. |
| author_facet | Benedetti, Valentin Casini, Horacio Magan, Javier M. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_03264 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | ABJ anomaly as a U(1) symmetry and Noether's theorem Benedetti, Valentin Casini, Horacio Magan, Javier M. High Energy Physics - Theory High Energy Physics - Phenomenology 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. |
| title | ABJ anomaly as a U(1) symmetry and Noether's theorem |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2309.03264 |