  In [1], we demonstrated that the structure function $g_1(x_B,Q^2)$ measured
in polarized deeply inelastic scattering (DIS) is dominated by the triangle
anomaly in both the Bjorken limit of large $Q^2$ and the Regge limit of small
$x_B$. In the worldline formulation of quantum field theory, the triangle
anomaly arises from the imaginary part of the worldline effective action. We
show explicitly how a Wess-Zumino-Witten term coupling the topological charge
density to a primordial isosinglet ${\bar \eta}$ arises in this framework. We
demonstrate the fundamental role played by this contribution both in
topological mass generation of the $\eta^\prime$ and in the cancellation of the
off-forward pole arising from the triangle anomaly in the proton's helicity
$\Sigma(Q^2)$. We recover the striking result by Shore and Veneziano that
$\Sigma\propto \sqrt{\chi'(0)}$, where $\chi'$ is the slope of the QCD
topological susceptibility in the forward limit. We construct an axion-like
effective action for $g_1$ at small $x_B$ that describes the interplay between
gluon saturation and the topology of the QCD vacuum. In particular, we outline
the role of "over-the-barrier" sphaleron-like transitions in spin diffusion at
small $x_B$. Such topological transitions can be measured in polarized DIS at a
future Electron-Ion Collider.
