M(atrix)-Theory in Various Dimensions

TL;DR

The paper validates M(atrix)-Theory as a nonperturbative formulation of M-Theory by demonstrating exact numerical agreement between long-range graviton interactions in 11D supergravity and D0-brane interactions in M(atrix)-Theory, both in flat space and under toroidal compactifications. It shows that wrapped membrane states are encoded in topological invariants of the reduced SYM bundles, with first and second Chern classes organizing 2- and 4-cycle wrappings, and that T-duality emerges naturally within this framework. The work extends the correspondence to include wrapped membranes and KK modes on $T^k$, deriving the correct $V(R)$ scaling, including logarithmic cases, and clarifying the role of UV/IR duality in the SYM description. Together these results strengthen the link between M(atrix)-Theory and M-Theory, and point toward generalizations to non-toroidal compactifications via topological data.

Abstract

We demonstrate the precise numerical correspondence between long range scattering of supergravitons and membranes in supergravity in the infinite momentum frame and in M(atrix)-Theory, both in 11 dimensions and for toroidal compactifications. We also identify wrapped membranes in terms of topological invariants of the vector bundles associated to the field theory description of compactified M(atrix)-Theory. We use these results to check the realization of T-duality in M(atrix)-Theory.