Membrane, Four-Brane and Dual Coordinates in the M(atrix) Theory Compactified on Tori

TL;DR

This paper derives gauge theories on dual tori from M(atrix) theory compactified on tori, revealing how dual coordinates and gauge couplings relate to torus volumes through explicit solutions.

Contribution

It provides explicit forms of solutions that connect membrane and four-brane configurations to dual gauge theories on tori, advancing understanding of compactification in M(atrix) theory.

Findings

Dual coordinates are explicitly derived from membrane and four-brane solutions.

Gauge couplings are shown to depend on the volume of dual tori.

The work establishes a link between matrix expansions and toroidal compactifications.

Abstract

In the M(atrix) theory by making the expansions of the matrices around the membrane and four-brane solutions we derive the three- and five-dimensional gauge theories on the dual tori. The explicit forms of solutions yield the dual coordinates and each expansion is related to a toroidal compactification of the M(atrix) theory. From the derived Lorentz and gauge invariant actions the gauge coupling constants are shown to be characterized by the volume of the dual tori.