  The mode of star formation that results in the formation of globular clusters
and young massive clusters is difficult to constrain through observations. We
present models of massive star cluster formation using the Torch framework,
which uses AMUSE to couple distinct multi-physics codes that handle star
formation, stellar evolution and dynamics, radiative transfer, and
magnetohydrodynamics. We upgrade Torch by implementing the N-body code PeTar,
thereby enabling Torch to handle massive clusters forming from $10^6\rm\,
M_\odot$ clouds with $\ge10^5$ individual stars. We present results from Torch
simulations of star clusters forming from $10^4, 10^5$, and $10^6\rm M_\odot$
turbulent, spherical gas clouds (named M4, M5, M6) of radius $R=11.7$ pc. We
find that star formation is highly efficient and becomes more so at higher
cloud mass and surface density. For M4, M5, and M6 with initial surface
densities $2.325\times 10^{1,2,3}\rm\, M_\odot\, pc^{-2}$, after a free-fall
time of $t_{ff}=6.7,2.1,0.67$ Myr, we find that $\sim30\%$, 40%, and 60% of the
cloud mass has formed into stars, respectively. The final integrated star
formation efficiency is $32\%,\, 65\%$, and 85\% for M4, M5, and M6.
Observations of nearby clusters similar to M4 have similar integrated star
formation efficiencies of $\leq30\%$. The M5 and M6 models represent a
different regime of cluster formation that is more appropriate for the
conditions in starburst galaxies and gas-rich galaxies at high redshift, and
that leads to a significantly higher efficiency of star formation. We argue
that young massive clusters build up through short efficient bursts of star
formation in regions that are sufficiently dense ($\ge 10^2
\rm\,M_\odot\,pc^{-2}$) and massive ($\ge10^5\rm\, M_\odot$). In such
environments, the dynamical time of the cloud becomes short enough that stellar
feedback cannot act quickly enough to slow star formation.
