Year: 2025
Type: article
Abstract: 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) 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) 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 0 -form symmetries cannot be non-invertible for d>2 d > 2 , and argue for a higher form-symmetry reconstruction theorem.
Source: SciPost Physics
Institution: Balseiro Institute
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4407104636