Deformation of half-BPS solution in ABJM model and instability of supermembrane

TL;DR

This paper investigates the instability of supermembranes and M2-branes by constructing explicit BPS solutions in the ABJM model and supermembrane theory, revealing zero modes indicative of potential deformations and instability.

Contribution

It explicitly constructs BPS solutions in both supermembrane and ABJM models, analyzing their fluctuations to understand M2-brane instability and its relation to D2-brane configurations.

Findings

Existence of zero modes indicating instability in M2-brane configurations.

Comparison showing no zero modes in D2-brane configurations under fixed string charge.

The Higgs mechanism relates ABJM solutions to D2-brane world volume theory.

Abstract

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.