Branes, fluxes and duality in M(atrix)-theory

We use the T-duality transformation which relates M-theory on T-3 to M-theory on a second T-3 with inverse volume to test the Banks-Fischler-Shenker-Susskind suggestion for the matrix model description of M-theory. We find evidence that T-duality is realized as S-duality for U(infinity) N = 4 Super-Yang-Mills in (3+1)D. We argue that Kaluza-Klein states of gravitons correspond to electric fluxes, wrapped membranes become magnetic fluxes and instantonic membranes are related to Yang-Mills instantons. The T-duality transformation of gravitons into wrapped membranes is interpreted as the duality between electric and magnetic fluxes. The identification of M-theory T-duality as SYM S-duality provides a natural framework for studying the M-theory 5-brane as the S-dual object to the unwrapped membrane. Using the equivalence between compactified M(atrix)-theory and SYM, we find a natural candidate for a description of the light-cone 5-brane of M-theory directly in terms of matrix variables, analogous to the known description of the M(atrix)-theory membrane. (C) 1997 Elsevier Science B.V.