Valentin Benedetti, Horacio Casini, Javier M. Magan
SciPost Phys. 18, 041 (2025) ·
published 3 February 2025
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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.
Dr Benedetti: "We thank the referee for the c..."
in Submissions | report on ABJ anomaly as a U(1) symmetry and Noether's theorem