Euler Top Dynamics of Nambu-Goto P-Branes

TL;DR

This paper introduces a method to find exact solutions for spinning p-branes in flat spacetime, modeling them as higher-dimensional Euler Tops, and explores their properties and reductions to string and membrane theories.

Contribution

It presents a novel approach to obtain exact solutions of spinning p-branes as higher-dimensional Euler Tops, including concrete examples and reductions to string and membrane models.

Findings

Exact solutions for spinning p-branes as Euler Tops.

Solutions for spherical and toroidal topologies.

Reduction to string and membrane Hamiltonians.

Abstract

We propose a method to obtain new exact solutions of spinning p-branes in flat space-times for any p, which manifest themselves as higher dimensional Euler Tops and minimize their energy functional. We provide concrete examples for the case of spherical topology S^{2}, S^{3} and rotational symmetry \prod_{i}SO(q_{i}). In the case of toroidal topology T^{2}, T^{3} the rotational symmetry is \prod SU(q_{i}) and m target dimensions are compactified on the torus T^{m} . By double dimensional reduction the Light Cone Hamiltonians of T^{2}, T^{3} reduce to those of closed string S^{1} and T^{2} membranes respectively. The solutions are interpreted as non-perturbative spinning soliton states of type IIA-IIB superstrings.