  Among the growing list of confirmed exoplanets, the number of planets
identified in dense star clusters remains sparse. Previous analyses have
suggested this may be due in part to dynamical interactions that unbind large
fractions of planets from their host stars, limiting the survival of planetary
systems in clusters. Thus, alternative detection strategies may be necessary to
study planets in clusters that may no longer be bound to a host star. Here, we
use the cluster Monte Carlo code CMC to explore the evolution of planetary
systems in dense star clusters. Depending on a number of initial conditions, we
show that $10-50\%$ of primordial planetary systems are broken through
dynamical encounters over a cluster's full lifetime, populating clusters with
"free-floating" planets. Furthermore, a large number ($30-80\%$) of planets are
ejected from their host cluster through strong dynamical encounters and/or
tidal loss. Additionally, we show that planets naturally mix with stellar-mass
black holes (BHs) in the central regions of their host cluster. As a
consequence, up to a few hundreds of planets will be tidally disrupted through
close passages of BHs. We show these BH-planet tidal disruption events (TDEs)
occur in clusters at a rate of up to $10^{-5}\,\rm{yr}^{-1}$ in a Milky
Way-type galaxy. We predict BH-planet TDEs should be detected by upcoming
transient surveys such as LSST at a rate of roughly a few events per year. The
observed rate of BH-planet TDEs would place new constraints upon the formation
and survival of both planetary systems and BHs in dense star clusters.
Additionally, depending on various assumptions including the initial number of
planets and their orbital properties, we predict that typical globular clusters
may contain a few dynamically-formed NS-planet systems at present as well as up
to roughly 100 dynamically-formed WD-planet systems.
