Conservation of supergravity currents from Matrix theory

In recent work by Kabat and Taylor, certain Matrix theory quantities have b een identified with the spatial moments of the supergravity stress-energy t ensor, membrane current, and fivebrane current. In this paper we determine the relations between these moments required by current conservation, and p rove that these relations held as exact Matrix theory identities at finite N. This establishes conservation of the effective supergravity currents (av eraged over the compact circle). In addition, the constraints of current co nservation allow us to deduce Matrix theory quantities corresponding to mom ents of the spatial current of the longitudinal fivebrane charge, not previ ously identified. (C) 1999 Elsevier Science B.V.