Anomalies for anomalous symmetries

Abstract

4d gauge theories with massless fermions typically have axial U(1) transformations that suffer from the ABJ anomaly. One can modify the theory of interest by adding more fields in a way that restores the axial symmetry, and use it to derive rigorous ’t Hooft anomaly matching conditions. These conditions are not valid for the original theory of interest, but for the modified theory. We show that the modification can be done in a specific way that allows us to relate the dynamics of the modified theory to the dynamics of the original theory. In this way, the anomaly matching conditions of the modified theory can be used to learn new things on the original theory even though they involve axial transformations which are not a symmetry of the original theory. We describe this method and discuss some applications to various examples.

On anomalies and gauging of U(1) non-invertible symmetries in 4d QED

“…In section 5 we explain why the procedure of 2 fails to work in other cases. Section 6 is a more general discussion about the relation between non-invertible symmetries and the ideas of [20]. These are two apparently different methods to promote the anomalous axial U(1) to an exact symmetry and use this symmetry to learn new things about the dynamics of the theory.…”

“…The idea to add new degrees of freedom in such a way to make the axial U(1) an exact symmetry was used before. In [20] it has been shown that by adding new heavy fields, it is possible to make a N discrete subgroup of the axial symmetry an exact symmetry of the theory. The effect of the heavy fields on the low energy theory is in the emergence of Chern-Simons terms on N domain walls.…”

Chiral gauge dynamics: candidates for non-supersymmetric dualities

“…The 't Hooft anomalies of these free fermions match in a rather striking fashion. Further work discussing various aspects of this theory can be found in [11][12][13][14][15][16].…”

From Skyrmions to One Flavored Baryons and Beyond

“…Now, we can compute the baryon current. We already know that (33) gives rise to the skyrmion current (14). We will compute the contribution from the hWZ action (43), including the improvement term (47).…”

“…The question of how a baryon in N f = 1 QCD can be described in terms of low energy degrees of freedom was an open question until the work of Komargodski in [9]. Later, this construction was elaborated and further studied in several papers, such as [10][11][12][13][14][15][16][17]. It was shown that there exist singular η configurations that carry baryon charge.…”