ABJ anomaly as a U(1) symmetry and Noether’s theorem
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 conser...
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2025-02-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.2.041 |
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| author | Valentin Benedetti, Horacio Casini, Javier M. Magan |
| author_facet | Valentin Benedetti, Horacio Casini, Javier M. Magan |
| author_sort | Valentin Benedetti, Horacio Casini, Javier M. Magan |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-5b9b5cc9de50474c817c3281f63143e5 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-5b9b5cc9de50474c817c3281f63143e52025-02-03T12:13:17ZengSciPostSciPost Physics2542-46532025-02-0118204110.21468/SciPostPhys.18.2.041ABJ anomaly as a U(1) symmetry and Noether’s theoremValentin Benedetti, Horacio Casini, Javier M. MaganThe 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.https://scipost.org/SciPostPhys.18.2.041 |
| spellingShingle | Valentin Benedetti, Horacio Casini, Javier M. Magan ABJ anomaly as a U(1) symmetry and Noether’s theorem SciPost Physics |
| title | ABJ anomaly as a U(1) symmetry and Noether’s theorem |
| title_full | ABJ anomaly as a U(1) symmetry and Noether’s theorem |
| title_fullStr | ABJ anomaly as a U(1) symmetry and Noether’s theorem |
| title_full_unstemmed | ABJ anomaly as a U(1) symmetry and Noether’s theorem |
| title_short | ABJ anomaly as a U(1) symmetry and Noether’s theorem |
| title_sort | abj anomaly as a u 1 symmetry and noether s theorem |
| url | https://scipost.org/SciPostPhys.18.2.041 |
| work_keys_str_mv | AT valentinbenedettihoraciocasinijaviermmagan abjanomalyasau1symmetryandnoetherstheorem |