  In this thesis, we propose a new consistency condition of quantum field
theory: Having an odd number of Majorana fermion zero modes on a dynamical
point-like soliton signifies an inconsistency in a theory with 3+1 or higher
dimensions. This inconsistency is related to the non-perturbative anomaly in
known models of quantum field theory. As an application, we check the
consistency of string and M theory compactifications with branes. We propose a
new criterion on the consistency of brane configurations: An odd number of
Majorana fermion zero modes on a D-brane stretching infinitely in space is
acceptable, whereas compactifying it to a point-like object leads to an
inconsistency. We show that a single M5-brane always has an even number of
Majorana fermion zero modes because of the symmetry on the worldvolume in 2+1
or higher dimensional compactifications of M-theory. We also construct models
with an odd number of Majorana fermion zero modes by intersecting D-branes.
From our criterion, compactifying such branes to point-like objects is not
allowed. Finally, we show that the gauge invariance on the intersecting branes
always requires an even number of Majorana fermion zero modes on a point-like
brane. This observation gives another interpretation of the inconsistency we
introduced.
