GAUGE-SYMMETRY IN EXTENDED OBJECTS AND THE STABILITY OF COMPACTIFIED MEMBRANES

A large number of gauge degrees of freedom inherent in relativistic extended objects often cause dynamical instability. This problem is studied by taking bosonic membranes and balls as examples. The bosonic membrane with two spatial coordinates compactified is examined in detail, and it is pointed out that the compactification produces a stabilizing potential barrier for the variables orthogonal to the compactified spaces. By gauge transforming away the variables in the compactified spaces, we suggest a possible confinement of unstable modes in compactified spaces.