  It is well-known that a supermembrane in the light-cone gauge has a
continuous spectrum and is unstable. Physical interpretation of this
instability is that a supermembrane can have a long thin tube without cost of
energy and consequently it becomes a spiky configuration in which multiple
membranes are connected by thin tubes. On the other hand, the ABJM model was
proposed as a low-energy description of multiple M2-branes in the static gauge.
It is natural that an M2-brane is also unstable in this gauge if we believe the
physical picture in the light-cone gauge. In order to examine this, we
construct a BPS solution explicitly both in the Nambu-Goto action of a
supermembrane in the static gauge and in the U(1){\times}U(1) ABJM model, which
represents intersecting M2-branes. Since this configuration is regarded as a
single M2-brane emitting another one, we study the instability of an M2-brane
by analyzing fluctuations around it. We show that a zero mode exists which can
deform the configuration. For comparison, we also examine a similar
configuration on the D2-brane and check that it does not have such zero modes
under a fixed string charge. Furthermore we confirm that the novel Higgs
mechanism translates our BPS solution in the ABJM model into that in the
D2-brane world volume theory, where the winding number of the former around the
fixed point of the orbifold becomes the number of strings ending on the
D2-brane in the latter.
