Exact solutions for U(1) globally invariant membranes

TL;DR

This paper derives exact solutions for U(1) invariant membranes, including static, contracting, and spinning configurations, in higher-dimensional Minkowski space, advancing understanding of membrane dynamics in theoretical physics.

Contribution

It provides the first general solutions for static and dynamic U(1) invariant membranes, including in the M-theory dimension D=11, and characterizes spinning membrane solutions with critical rotation frequency.

Findings

Exact static membrane solutions in D=2N+1 dimensions.

Time-dependent solutions with Jacobi elliptic functions for contracting membranes.

Spinning membrane solutions with a critical rotation frequency.

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.