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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2025-02-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.2.041 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2542-4653 |