Topological terms and anomaly matching in effective field theories on 3 x ?1. Part I. Abelian symmetries and intermediate scales

We explicitly calculate the topological terms that arise in IR effective field theories for SU(N) gauge theories on (3) x ?(1) by integrating out all but the lightest modes. We then show how these terms match all global-symmetry 't Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-U(1) anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chirallagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton 't Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.

Automated summary

This article explicitly calculates the topological terms that arise in SU(N) gauge theories under different field conditions and the matching conclusions, mainly involving theories with Abelian 0-form symmetry. Through comparative analysis, it is pointed out that the conclusion of anomaly matching differs from the previously thought form.