Extragalactic Star Cluster Science with the Nancy Grace Roman Space Telescope's High Latitude Wide Area Survey and the Vera C. Rubin Observatory

The Nancy Grace Roman Telescope's High Latitude Wide Area Survey will have a number of synergies with the Vera Rubin Observatory's Legacy Survey of Space and Time (LSST), particularly for extragalactic star clusters. Understanding the nature of star clusters and star cluster systems are key topics in many areas of astronomy, chief among them stellar evolution, high energy astrophysics, galaxy assembly/dark matter, the extragalactic distance scale, and cosmology. One of the challenges will be disentangling the age/metallicity degeneracy because young ($\sim$Myr) metal-rich clusters have similar SEDs to old ($\sim$Gyr) metal-poor clusters. Rubin will provide homogeneous, $ugrizy$ photometric coverage, and measurements in the red Roman filters will help break the age-metallicity and age-extinction degeneracies, providing the first globular cluster samples that cover wide areas while essentially free of contamination from Milky Way stars. Roman's excellent spatial resolution will also allow measurements of cluster sizes. We advocate for observations of a large sample of galaxies with a range of properties and morphologies in the Rubin/LSST footprint matching the depth of the LSST Wide-Fast-Deep field $i$ band limit (26.3 mag), and recommend adding the F213 filter to the survey.