INTERACTIONS BETWEEN BRANES AND MATRIX THEORIES

We review some tests of the O-brane and instanton matrix models based on comparing long-distance interaction potentials between branes and t heir bound states (with 1/2,1/4 or 1/8 of supersymmetry) in supergravi ty and in super Yang-Mills descriptions. We first consider the supergr avity-SYM correspondence at the level of the leading term in the inter action potential, and then describe some recent results concerning the subleading term and their implications for the structure of the 2-loo p F-6 term in the SYM effective action.