Anomaly equation of the large U(1) chiral symmetry

In this study, we first heuristically construct the charges corresponding to the chiral transformation associated with the large U(1) gauge symmetry. We refer to these as the large chiral charges, and to the chiral transformation they generate as the large chiral transformations. Then, showing that these large chiral charges can be obtained based on Noether's theorem, we obtain the anomaly equation associated with these large chiral transformations. Subsequently, considering the one-loop diagrams of the fermionic field coupled to multiple classical gauge fields (which constitute the effective action of the model in this study with regard to the gauge field), we perform an axialization. Then, defining the BRS transformations for the large U(1) gauge symmetry (we refer to these as the large BRS transformations), we perform these transformations to these axialized one-loop diagrams, and demonstrate that the anomaly equations mentioned above can be derived by evaluating these diagrams. We further confirm that these anomaly equations can be derived using the Fujikawa method. Finally, we discuss the breaking of unitarity and the low-energy effective model associated with the large chiral anomaly in this study, and comment on potential future developments arising from them.