  We present a SU(2) gauge theory of fluctuating magnetic order in the
two-dimensional Hubbard model. The theory is based on a fractionalization of
electrons in fermionic chargons and bosonic spinons. The chargons undergo
N\'eel or spiral magnetic order below a density dependent transition
temperature $T^*$. Fluctuations of the spin orientation are described by a
non-linear sigma model obtained from a gradient expansion of the spinon action.
The spin stiffnesses are computed from a renormalization group improved random
phase approximation. Our approximations are applicable for a weak or moderate
Hubbard interaction. The spinon fluctuations prevent magnetic long-range order
of the electrons at any finite temperature. The phase with magnetic chargon
order exhibits many features characterizing the pseudogap regime in high-$T_c$
cuprates: a strong reduction of charge carrier density, a spin gap, Fermi arcs,
and electronic nematicity.
