Conservation of Supergravity Currents from Matrix Theory

TL;DR

This paper proves that Matrix Theory accurately encodes supergravity current conservation laws at finite N, establishing precise relations between Matrix Theory quantities and supergravity currents, including new identifications for fivebrane charge moments.

Contribution

It demonstrates that current conservation relations are exact identities in Matrix Theory at finite N, and identifies new Matrix Theory quantities related to fivebrane charge moments.

Findings

Conservation relations hold exactly at finite N.

Matrix Theory quantities match supergravity current moments.

New identifications for fivebrane charge moments are established.

Abstract

In recent work by Kabat and Taylor, certain Matrix theory quantities have been identified with the spatial moments of the supergravity stress-energy tensor, membrane current, and fivebrane current. In this note, we determine the relations between these moments required by current conservation, and prove that these relations hold as exact Matrix Theory identities at finite N. This establishes conservation of the effective supergravity currents (averaged over the compact circle). In addition, the constraints of current conservation allow us to deduce Matrix theory quantities corresponding to moments of the spatial current of the longitudinal fivebrane charge, not previously identified.