String Theory Journal Club

The Adler-Bell-Jackiw anomaly determines the violation of chiral symmetry when massless fermions are coupled to an abelian gauge field. In his 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. In this talk we show this internal U(1) symmetry transforms the Haag duality violating sectors (or non local operator classes), and explain how 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. If time permits we will comment on recent literature where this symmetry is considered to be either absent or non-invertible.