Rotating Toroidal Branes in Supermembrane and Matrix Theory

TL;DR

This paper explores rotating toroidal membrane solutions within supermembrane and Matrix theory frameworks, revealing stable configurations in higher dimensions and their correspondence to bound states of D0-branes.

Contribution

It introduces new rotating toroidal membrane solutions in six dimensions, analyzes their stability, and connects them to D0-brane bound states in Matrix Theory.

Findings

Existence of stable six-dimensional rotating toroidal membrane solutions.

Representation of angular momentum via U(1) charges.

Correspondence to toroidal D0-brane bound states.

Abstract

In the lightcone frame, where the supermembrane theory and the Matrix model are strikingly similar, the equations of motion admit an elegant complexification in even dimensional spaces. Although the explicit rotational symmetry of the target space is lost, the remaining unitary symmetries apart from providing a simple and unifying description of all known solutions suggest new ones for rotating spherical and toroidal membranes. In this framework the angular momentum is represented by U(1) charges which balance the nonlinear attractive forces of the membrane. We examine in detail a six dimensional rotating toroidal membrane solution which lives in a 3-torus, $T^3$ and admits stable radial modes. In Matrix Theory it corresponds to a toroidal N-$D_{0}$ brane bound state. We demonstrate its existence and discuss its radial stability.