  We study the low energy effective theory of two sets of D3-branes overlapping
in 1+1 dimensions, recently considered by Mintun, Polchinski, and Sun. In the
original treatment by MPS, by studying the properties of magnetic solitons, the
low energy effective field theory was found to require some ultraviolet
completion, possibly involving full string dynamics. Recently in a companion
paper, it was shown that by scaling the angle between the D3-branes and the
D3'-branes in the zero slope limit in specific way, one can find simpler
effective field theory which consists of a single tower of Regge trajectory
states and yet is ultraviolet complete and non-singular. In this article, we
study this model by further studying a limit which recovers the MPS dynamics
from this non-singular construction. We approach this issue from a holographic
perspective, where we consider a stack of $N$ D3-branes overlapping with a
single D3'-brane, and treat that D3'-brane as a probe in the $AdS_5 \times S^5$
dual. In general, the D3'-brane probe supports a magnetic monopole as a
non-singular soliton configuration, but in the limit where the MPS dynamics is
recovered, the soliton degenerates. This is consistent with the idea that the
effective dynamics in the MPS setup is incomplete, but that it can be completed
with a single tower of Regge trajectory states.
