  Over a hundred millisecond radio pulsars (MSPs) have been observed in
globular clusters (GCs), motivating theoretical studies of the formation and
evolution of these sources through stellar evolution coupled to stellar
dynamics. Here we study MSPs in GCs using realistic $N$-body simulations with
our Cluster Monte Carlo code. We show that neutron stars (NSs) formed in
electron-capture supernovae (including both accretion-induced and
merger-induced collapse of white dwarfs) can be spun up through mass transfer
to form MSPs. Both NS formation and spin-up through accretion are greatly
enhanced through dynamical interaction processes. We find that our models for
average GCs at the present day with masses $\approx 2 \times 10^5\,M_\odot$ can
produce up to $10-20$ MSPs, while a very massive GC model with mass $\approx
10^6\,M_\odot$ can produce close to $100$. We show that the number of MSPs is
anti-correlated with the total number of stellar-mass black holes (BHs)
retained in the host cluster. The radial distributions are also affected: MSPs
are more concentrated towards the center in a host cluster with a smaller
number of retained BHs. As a result, the number of MSPs in a GC could be used
to place constraints on its BH population. Some intrinsic properties of MSP
systems in our models (such as the magnetic fields and spin periods) are in
good overall agreement with observations, while others (such as the
distribution of binary companion types) less so, and we discuss the possible
reasons for such discrepancies. Interestingly, our models also demonstrate the
possibility of dynamically forming NS--NS and NS--BH binaries in GCs, although
the predicted numbers are very small.
