Aharonov-Bohm in the Sky : A CMB Millikan Experiment with Cosmic Axiverse Strings

We show that photons moving around an axion string coupled to photons undergo an Aharonov-Bohm effect.  As a result, axion strings produce a distinct quantized polarization rotation of CMB photons which can be as large as O(1%).  As the CMB passes many strings, this polarization rotation converts E-modes to B-modes and adds up like a random walk.  We show that the expected size of the final result is well within the reach of current and future CMB experiments.  The quantized polarization rotation angle is topological in nature and its value provides insight into the quantization of electric charge.