  We study axion strings of hyperlight axions coupled to photons. Hyperlight
axions -- axions lighter than Hubble at recombination -- are a generic
prediction of the string axiverse. These axions strings produce a distinct
quantized polarization rotation of CMB photons which is
$\mathcal{O}(\alpha_{\rm em})$. As the CMB light passes many strings, this
polarization rotation converts E-modes to B-modes and adds up like a random
walk. Using numerical simulations we show that the expected size of the final
result is well within the reach of current and future CMB experiments through
the measurement of correlations of CMB B-modes with E- and T-modes. The
quantized polarization rotation angle is topological in nature and can be seen
as a geometric phase. Its value depends only on the anomaly coefficient and is
independent of other details such as the axion decay constant. Measurement of
the anomaly coefficient by measuring this rotation will provide information
about the UV theory, such as the quantization of electric charge and the value
of the fundamental unit of charge. The presence of axion strings in the
universe relies only on a phase transition in the early universe after
inflation, after which the string network rapidly approaches an attractor
scaling solution. If there are additional stable topological objects such as
domain walls, axions as heavy as $10^{-15}$ eV would be accessible. The
existence of these strings could also be probed by measuring the relative
polarization rotation angle between different images in gravitationally lensed
quasar systems.
