Longitudinal 5-branes as 4-spheres in Matrix theory

TL;DR

This paper constructs longitudinal 5-branes in Matrix theory with a geometry resembling a 4-sphere, demonstrating their properties align with expectations from M-theory and 11D supergravity.

Contribution

It introduces an explicit matrix-based construction of 5-branes with 4-sphere geometry in Matrix theory, extending previous membrane models.

Findings

Matrices exhibit properties consistent with 4-sphere geometry

Energy and interactions match 11D supergravity predictions

Construction valid for an infinite series of N values

Abstract

We present a construction in Matrix theory of longitudinal 5-branes whose geometry in transverse space corresponds to a 4-sphere. We describe these branes through an explicit construction in terms of N*N matrices for a particular infinite series of values of N. The matrices used in the construction have a number of properties which can be interpreted in terms of the 4-sphere geometry, in analogy with similar properties of the SU(2) generators used in the construction of a spherical membrane. The physical properties of these systems correspond with those expected from M-theory; in particular, these objects have an energy and a leading long-distance interaction with gravitons which agrees with 11D supergravity at leading order in N.