  We explicitly calculate the topological terms that arise in IR effective
field theories for $SU(N)$ gauge theories on $\mathbb{R}^3 \times S^1$ 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 chiral-lagrangian 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.
