Supergravity currents and linearized interactions for matrix theory configurations with fermionic backgrounds

The leading terms in the long-range interaction potential between an arbitr ary pair of matrix theory objects are calculated at one-loop order. This re sult generalizes previous calculations by including arbitrary fermionic bac kground field configurations. The interaction potential at orders 1/r(7) an d 1/r(8) is shown to correspond precisely with the leading terms expected f rom linearized supergravity interactions between arbitrary objects in M-the ory. General expressions for the stress tensor, membrane current and 5-bran e current of an arbitrary matrix configuration are derived, including fermi onic contributions. Supergravity effects which are correctly reproduced inc lude membrane/5-brane interactions, 0-brane/6-brane interactions, supercurr ent/supercurrent interactions and the spin contributions to moments of the supergravity currents. The matrix theory description of the supergravity st ress tensor, membrane current and 5-brane current are used to propose an ex plicit formulation of matrix theory in an arbitrary background metric and 3 -form field.