  Studying spin-momentum correlations in hadronic collisions offers a glimpse
into a three-dimensional picture of proton structure. The transverse
single-spin asymmetry for midrapidity isolated direct photons in $p^\uparrow+p$
collisions at $\sqrt{s}=200$ GeV is measured with the PHENIX detector at the
Relativistic Heavy Ion Collider (RHIC). Because direct photons in particular
are produced from the hard scattering and do not interact via the strong force,
this measurement is a clean probe of initial-state spin-momentum correlations
inside the proton and is in particular sensitive to gluon interference effects
within the proton. This is the first time direct photons have been used as a
probe of spin-momentum correlations at RHIC. The uncertainties on the results
are a fifty-fold improvement with respect to those of the one prior measurement
for the same observable, from the Fermilab E704 experiment. These results
constrain gluon spin-momentum correlations in transversely polarized protons.
