TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.2.041
TI  - ABJ anomaly as a U(1) symmetry and Noether’s theorem
PY  - 2025/02/03
UR  - https://www.scipost.org/SciPostPhys.18.2.041
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 2
SP  - 041
A1  - Benedetti, Valentin
AU  - Casini, Horacio
AU  - Magan, Javier
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.18.2.041,
	title={{ABJ anomaly as a U(1) symmetry and Noether’s theorem}},
	author={Valentin Benedetti and Horacio Casini and Javier M. Magan},
	journal={SciPost Phys.},
	volume={18},
	pages={041},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.2.041},
	url={https://scipost.org/10.21468/SciPostPhys.18.2.041},
}