  There is evidence that the pseudogap phase in the cuprates breaks
time-reversal symmetry. Here we show that pair density wave (PDW) states give
rise to a translational invariant nonsuperconducting order parameter that
breaks time-reversal and parity symmetries, but preserves their product. This
secondary order parameter has a different origin, but shares the same symmetry
properties as a magnetoelectric loop current order that has been proposed
earlier in the context of the cuprates to explain the appearance of intracell
magnetic order. We further show that, due to fluctuations, this secondary loop
current order, which breaks only discrete symmetries, can preempt PDW order,
which breaks both continuous and discrete symmetries. In such a phase, the
emergent loop current order coexists with spatial short-range superconducting
order and possibly short-range charge density wave (CDW) order. Finally, we
propose a PDW phase that accounts for intracell magnetic order and the Kerr
effect, has CDW order consistent with x-ray scattering and nuclear magnetic
resonance observations, and quasi-particle properties consistent with
angle-resolved photoemission scattering.
