Exact solutions for U(1) globally invariant membranes

Abstract

The exact solvability problem of the nonlinear equations describing the U(1) invariant membranes is studied and the general solution for the static membrane in D=2N+1-dimensional Minkowski space-time, including M-theory case D=11, is obtained. The time-dependent Jacobi elliptic function solution describing a family of contracting tori is also found, together with the solution corresponding to a spinning torus characterized by the presence of the critical rotation frequency Omega=T^{1/3}/pi^{1/2} expressed via the membrane tension T.

16 pages, published in PLB

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• The eleven-dimensional supermembrane revisited
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• Spinning solutions for the bosonic M2-brane with $C_{\pm }$ fluxes
• Inflation versus collapse in brane matter
• $p$-Branes with $Ad{S}_{p+1}$ vacuum as models of $R^2$ gravity
• On brane symmetries
• Dirac membrane and hadrons
• Dirac equation for embedded 4-geometries