The continuous cadence Roman Galactic Bulge survey

Galactic binaries with orbital periods less than 1 hour are strong gravitational wave sources in the mHz regime, ideal for the Laser Interferometer Space Antenna (LISA). At least several hundred, maybe up to a thousand of those binaries are predicted to be sufficiently bright in electromagnetic wavebands to allow detection in both the electromagnetic and the gravitational bands allowing us to perform multi-messenger studies on a statistically significant sample. Theory predicts that a large number of these sources will be located in the Galactic Plane and in particular towards the Galactic Bulge region. Some of these tight binaries may host sub-stellar tertiaries. In this white paper we propose an observing strategy for the Galactic Bulge Time Domain Survey which would use the unique observing capabilities of the Nancy Grace Roman Space telescope to discover and study several 10s of new strong LISA gravitational sources as well as exoplanet candidates around compact white dwarf binaries and other short period variables such as flaring stars, compact pulsators and rotators.