  The nucleon axial charge is a central ingredient in nuclear and particle
physics, and a key observable in precision tests of the electroweak Standard
Model sector and beyond. We report on the first complete calculation of its
electroweak quantum corrections up to $\mathcal{O}(\alpha)$, using a
combination of current algebra techniques and QCD sum rules. We find a
substantial enhancement due to the weak magnetism contribution in the elastic
channel, and include higher-twist and target mass corrections at low $Q^2$ to
find $\Delta_R^A = 0.02881(22)$. Using analogous methods, we determine a new
value for the vector charge renormalization, $\Delta_R^V = 0.02474(27)$, and
show how the two most recent calculations can be brought into agreement. This
allows us to determine a corrected experimental $g_A^0 = 1.2730(13)$, which is
a $>2\sigma$ shift away from the commonly quoted value. We use this new result
to set constraints on exotic right-handed currents by comparing to lattice QCD
results, and resolve a double-counting issue in the $|V_{ud}|$ extraction from
mirror decays.
