As of August 2019, among the more than 4000 confirmed exoplanets, only one has been detected in a globular cluster (GC) M4. The scarce of exoplanet detections motivates us to employ direct $N$-body simulations to investigate the dynamical stability of planets in young massive clusters (YMCs), which are potentially the progenitors of GCs. In an $N=128{rm k}$ cluster of virial radius 1.7 pc (comparable to Westerlund-1), our simulations show that most wide-orbit planets ($ageq 20$~au) will be ejected within a timescale of 10 Myr. Interestingly, more than $70%$ of planets with $a<5$~au survive in the 100 Myr simulations. Ignoring planet-planet scattering and tidal damping, the survivability at $t$ Myr as a function of initial semi-major axis $a_0$ in au in such a YMC can be described as $f_{rm surv}(a_0, t)=-0.33 log_{10}(a_0) left(1 - e^{-0.0482t} right) + 1$. Upon ejection, about $28.8%$ of free-floating planets (FFPs) have sufficient speeds to escape from the host cluster at a crossing timescale. The other FFPs will remain bound to the cluster potential, but the subsequent dynamical evolution of the stellar system can result in the delayed ejection of FFPs from the host cluster. Although a full investigation of planet population in GCs requires extending the simulations to multi-Gyr, our results suggest that wide-orbit planets and free-floating planets are unlikely to be found in GCs.
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