  Orbital magnetism and the loop currents (LC) that accompany it have been
proposed to emerge in many systems, including cuprates, iridates, and kagome
superconductors. In the case of cuprates, LCs have been put forward as the
driving force behind the pseudogap, strange-metal behavior, and
$d_{x^2-y^2}$-wave superconductivity. Here, we investigate whether fluctuating
intra-unit-cell loop currents can cause unconventional superconductivity. For
odd-parity LCs, we find that they are strongly repulsive in all pairing
channels near the underlying quantum-critical point (QCP). For even-parity LCs,
their fluctuations do give rise to unconventional pairing. However, this
pairing is not amplified in the vicinity of the QCP, in sharp contrast to other
known cases of pairing mediated by intra-unit-cell order parameters, such as
spin-magnetic, nematic, or ferroelectric ones. Applying our formalism to the
cuprates, we conclude that pairing mediated by fluctuating intra-unit-cell LCs
is unlikely to yield $d_{x^2-y^2}$-wave superconductivity. We also show that
loop currents, if relevant for the cuprates, must vary between unit cells and
break translation symmetry.
